96:@0.058194:0.966765:0.075166:0.966765:0.075166:0.950778:0.058194:0.950778:0.000000:0.000000
M.5.2.16. Describir la hipérbola como lugares geométricos en el plano.  :@0.143845:0.936790:0.449098:0.936790:0.449098:0.926748:0.143845:0.926748:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.2.17. Escribir y reconocer las ecuaciones cartesianas de la hipérbola con centro en el origen y con centro fuera del origen para resolver y plantear problemas (por ejemplo, :@0.143845:0.945591:0.894262:0.945591:0.894262:0.935549:0.143845:0.935549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en física: órbitas planetarias, tiro parabólico, etc.), identificando la validez y pertinencia de los resultados obtenidos.:@0.143845:0.954392:0.637271:0.954392:0.637271:0.944350:0.143845:0.944350:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ecuación cartesiana de la hipérbola:@0.404235:0.113410:0.842980:0.113410:0.842980:0.068750:0.404235:0.068750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Hipérbola:@0.404236:0.136533:0.484545:0.136533:0.484545:0.118850:0.404236:0.118850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.404236:0.153703:0.484320:0.153703:0.484320:0.136757:0.404236:0.136757:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean  ,  ,     :@0.484322:0.153240:0.591174:0.153240:0.591174:0.136743:0.484322:0.136743:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b c:@0.529017:0.153356:0.568241:0.153356:0.568241:0.136887:0.529017:0.136887:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.572380:0.152722:0.587032:0.152722:0.587032:0.139349:0.572380:0.139349:0.000000
:@0.591175:0.152154:0.604479:0.152154:0.604479:0.139291:0.591175:0.139291:0.000000
+:@0.604478:0.146887:0.610778:0.146887:0.610778:0.137269:0.604478:0.137269:0.000000
, tal que 0 <   <    y   =   –  ,:@0.610780:0.153240:0.834970:0.153240:0.834970:0.136743:0.610780:0.136743:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a c:@0.698552:0.153356:0.733808:0.153356:0.733808:0.136887:0.698552:0.136887:0.000000:0.000000:0.000000
b:@0.754056:0.153356:0.763322:0.153356:0.763322:0.136887:0.754056:0.136887:0.000000
2:@0.763319:0.146887:0.768272:0.146887:0.768272:0.137269:0.763319:0.137269:0.000000
a:@0.787363:0.153356:0.796340:0.153356:0.796340:0.136887:0.787363:0.136887:0.000000
2:@0.796339:0.146887:0.801293:0.146887:0.801293:0.137269:0.796339:0.137269:0.000000
c:@0.820077:0.153356:0.827263:0.153356:0.827263:0.136887:0.820077:0.136887:0.000000
2:@0.827263:0.146887:0.832216:0.146887:0.832216:0.137269:0.827263:0.137269:0.000000
F:@0.404237:0.170707:0.411789:0.170707:0.411789:0.154238:0.404237:0.154238:0.000000
:@0.406395:0.168567:0.412810:0.168567:0.412810:0.152749:0.406395:0.152749:0.000000
1:@0.411267:0.173868:0.416220:0.173868:0.416220:0.164250:0.411267:0.164250:0.000000
 = (– , 0),    = ( , 0). Se le llama hipérbola de eje principal al eje   , y fo-:@0.416221:0.170591:0.891778:0.170591:0.891778:0.154094:0.416221:0.154094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.450550:0.170707:0.457735:0.170707:0.457735:0.154238:0.450550:0.154238:0.000000
F:@0.488292:0.170707:0.495844:0.170707:0.495844:0.154238:0.488292:0.154238:0.000000
:@0.490450:0.168567:0.496865:0.168567:0.496865:0.152749:0.490450:0.152749:0.000000
2:@0.495327:0.173868:0.500281:0.173868:0.500281:0.164250:0.495327:0.164250:0.000000
c:@0.523534:0.170707:0.530720:0.170707:0.530720:0.154238:0.523534:0.154238:0.000000
x:@0.844975:0.170707:0.852450:0.170707:0.852450:0.154238:0.844975:0.154238:0.000000
cos    y  , al conjunto de puntos del plano definido y denotado como::@0.404244:0.187942:0.891836:0.187942:0.891836:0.171444:0.404244:0.171444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F:@0.430656:0.188058:0.438208:0.188058:0.438208:0.171589:0.430656:0.171589:0.000000
:@0.432814:0.185918:0.439229:0.185918:0.439229:0.170100:0.432814:0.170100:0.000000
1:@0.437672:0.191219:0.442625:0.191219:0.442625:0.181601:0.437672:0.181601:0.000000
F:@0.461371:0.188058:0.468923:0.188058:0.468923:0.171589:0.461371:0.171589:0.000000
:@0.463510:0.185918:0.469925:0.185918:0.469925:0.170100:0.463510:0.170100:0.000000
2:@0.468379:0.191219:0.473333:0.191219:0.473333:0.181601:0.468379:0.181601:0.000000
ℋ:@0.467786:0.225191:0.484198:0.225191:0.484198:0.207056:0.467786:0.207056:0.000000
(0,  ,  ) =         |     – :@0.484199:0.218117:0.671767:0.218117:0.671767:0.201620:0.484199:0.201620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.491423:0.216093:0.497839:0.216093:0.497839:0.200275:0.491423:0.200275:0.000000
a b:@0.504639:0.218233:0.529780:0.218233:0.529780:0.201764:0.504639:0.201764:0.000000:0.000000:0.000000
x:@0.563109:0.218233:0.570584:0.218233:0.570584:0.201764:0.563109:0.201764:0.000000
:@0.564805:0.218609:0.571220:0.218609:0.571220:0.202791:0.564805:0.202791:0.000000
:@0.575360:0.217599:0.590013:0.217599:0.590013:0.204225:0.575360:0.204225:0.000000
:@0.594155:0.217030:0.607460:0.217030:0.607460:0.204168:0.594155:0.204168:0.000000
2:@0.607460:0.211764:0.612413:0.211764:0.612413:0.202146:0.607460:0.202146:0.000000
| ||:@0.625705:0.218855:0.644873:0.218855:0.644873:0.199057:0.625705:0.199057:0.000000:0.000000:0.000000:0.000000
x:@0.644873:0.218233:0.652348:0.218233:0.652348:0.201764:0.644873:0.201764:0.000000
:@0.646568:0.218609:0.652983:0.218609:0.652983:0.202791:0.646568:0.202791:0.000000
F:@0.671767:0.218233:0.679319:0.218233:0.679319:0.201764:0.671767:0.201764:0.000000
:@0.673925:0.216093:0.680340:0.216093:0.680340:0.200275:0.673925:0.200275:0.000000
1:@0.678798:0.221394:0.683751:0.221394:0.683751:0.211776:0.678798:0.211776:0.000000
|| ||:@0.683752:0.218855:0.722570:0.218855:0.722570:0.199057:0.683752:0.199057:0.000000:0.000000:0.000000:0.000000:0.000000
 –   – :@0.693770:0.218117:0.749465:0.218117:0.749465:0.201620:0.693770:0.201620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.722570:0.218233:0.730045:0.218233:0.730045:0.201764:0.722570:0.201764:0.000000
:@0.724266:0.218609:0.730681:0.218609:0.730681:0.202791:0.724266:0.202791:0.000000
F:@0.749465:0.218233:0.757017:0.218233:0.757017:0.201764:0.749465:0.201764:0.000000
:@0.751622:0.216093:0.758038:0.216093:0.758038:0.200275:0.751622:0.200275:0.000000
2:@0.756496:0.221394:0.761449:0.221394:0.761449:0.211776:0.756496:0.211776:0.000000
|| |:@0.761449:0.218855:0.780618:0.218855:0.780618:0.199057:0.761449:0.199057:0.000000:0.000000:0.000000:0.000000
 = 2   .:@0.780617:0.218117:0.828222:0.218117:0.828222:0.201620:0.780617:0.201620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.808205:0.218233:0.817183:0.218233:0.817183:0.201764:0.808205:0.201764:0.000000
Claramente,  (0,  ,  )    .:@0.404232:0.248293:0.606412:0.248292:0.606412:0.231795:0.404232:0.231795:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℋ:@0.493820:0.255367:0.510231:0.255367:0.510231:0.237231:0.493820:0.237231:0.000000
:@0.517456:0.246268:0.523872:0.246268:0.523872:0.230450:0.517456:0.230450:0.000000
a b:@0.530672:0.248408:0.555814:0.248408:0.555814:0.231939:0.530672:0.231939:0.000000:0.000000:0.000000
:@0.565907:0.247925:0.581257:0.247925:0.581257:0.233915:0.565907:0.233915:0.000000
:@0.585400:0.247205:0.598705:0.247205:0.598705:0.234343:0.585400:0.234343:0.000000
2:@0.598703:0.241939:0.603656:0.241939:0.603656:0.232321:0.598703:0.232321:0.000000
En muchos libros de geometría analítica, se define a la hipérbola :@0.404242:0.278468:0.895886:0.278468:0.895886:0.261971:0.404242:0.261971:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como el conjunto de puntos   del plano, tal que el valor absoluto de :@0.404242:0.295819:0.895911:0.295819:0.895911:0.279321:0.404242:0.279321:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.612904:0.295935:0.620379:0.295935:0.620379:0.279466:0.612904:0.279466:0.000000
:@0.614599:0.296311:0.621015:0.296311:0.621015:0.280493:0.614599:0.280493:0.000000
las diferencias de las distancias de   a   y   a   es una constante dada. :@0.404242:0.313170:0.895909:0.313169:0.895909:0.296671:0.404242:0.296672:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x F:@0.641667:0.313285:0.672414:0.313285:0.672414:0.296817:0.641667:0.296817:0.000000:0.000000:0.000000
:@0.643362:0.313661:0.649778:0.313661:0.649778:0.297843:0.643362:0.297843:0.000000
:@0.667020:0.311146:0.673435:0.311146:0.673435:0.295327:0.667020:0.295327:0.000000
1:@0.671889:0.314560:0.676842:0.314560:0.676842:0.304942:0.671889:0.304942:0.000000
x F:@0.691908:0.313285:0.722656:0.313285:0.722656:0.296816:0.691908:0.296816:0.000000:0.000000:0.000000
:@0.693604:0.313661:0.700019:0.313661:0.700019:0.297843:0.693604:0.297843:0.000000
:@0.717261:0.311145:0.723677:0.311145:0.723677:0.295327:0.717261:0.295327:0.000000
2:@0.722138:0.315189:0.727091:0.315189:0.727091:0.305570:0.722138:0.305570:0.000000
La distancia del punto   a   es ||   –   || y la distancia del punto   a :@0.404243:0.330520:0.895916:0.330520:0.895916:0.314022:0.404243:0.314022:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x F:@0.567003:0.330636:0.599564:0.330636:0.599564:0.314167:0.567003:0.314167:0.000000:0.000000:0.000000
:@0.568672:0.331012:0.575087:0.331012:0.575087:0.315193:0.568672:0.315193:0.000000
:@0.594160:0.328496:0.600575:0.328496:0.600575:0.312678:0.594160:0.312678:0.000000
1:@0.599031:0.333797:0.603985:0.333797:0.603985:0.324178:0.599031:0.324178:0.000000
x:@0.641994:0.330636:0.649469:0.330636:0.649469:0.314167:0.641994:0.314167:0.000000
:@0.643689:0.331012:0.650104:0.331012:0.650104:0.315193:0.643689:0.315193:0.000000
F:@0.669697:0.330636:0.677249:0.330636:0.677249:0.314167:0.669697:0.314167:0.000000
:@0.671836:0.328496:0.678251:0.328496:0.678251:0.312678:0.671836:0.312678:0.000000
1:@0.676704:0.333797:0.681657:0.333797:0.681657:0.324178:0.676704:0.324178:0.000000
x:@0.871285:0.330636:0.878760:0.330636:0.878760:0.314167:0.871285:0.314167:0.000000
:@0.872981:0.331012:0.879396:0.331012:0.879396:0.315193:0.872981:0.315193:0.000000
F:@0.404238:0.347986:0.411790:0.347986:0.411790:0.331518:0.404238:0.331518:0.000000
:@0.406396:0.345846:0.412811:0.345846:0.412811:0.330028:0.406396:0.330028:0.000000
2:@0.411267:0.351147:0.416220:0.351147:0.416220:0.341529:0.411267:0.341529:0.000000
 es ||  –  ||, con lo que la hipérbola es el conjunto de puntos   del :@0.416221:0.347871:0.895915:0.347871:0.895915:0.331373:0.416221:0.331373:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.449511:0.347986:0.456986:0.347986:0.456986:0.331518:0.449511:0.331518:0.000000
:@0.451207:0.348362:0.457622:0.348362:0.457622:0.332544:0.451207:0.332544:0.000000
F:@0.477022:0.347986:0.484574:0.347986:0.484574:0.331518:0.477022:0.331518:0.000000
:@0.479180:0.345846:0.485595:0.345846:0.485595:0.330028:0.479180:0.330028:0.000000
2:@0.484060:0.351147:0.489013:0.351147:0.489013:0.341529:0.484060:0.341529:0.000000
x:@0.857710:0.347986:0.865185:0.347986:0.865185:0.331518:0.857710:0.331518:0.000000
:@0.859426:0.348362:0.865842:0.348362:0.865842:0.332544:0.859426:0.332544:0.000000
plano, tal que ||  –  || – ||   –  || es una constante dada, la cual se :@0.404246:0.365221:0.895862:0.365221:0.895862:0.348724:0.404246:0.348724:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.516888:0.365337:0.524363:0.365337:0.524363:0.348868:0.516888:0.348868:0.000000
:@0.518605:0.365713:0.525020:0.365713:0.525020:0.349895:0.518605:0.349895:0.000000
F:@0.545191:0.365337:0.552743:0.365337:0.552743:0.348868:0.545191:0.348868:0.000000
:@0.547368:0.363197:0.553783:0.363197:0.553783:0.347379:0.547368:0.347379:0.000000
1:@0.552229:0.368498:0.557182:0.368498:0.557182:0.358880:0.552229:0.358880:0.000000
x:@0.602223:0.365337:0.609698:0.365337:0.609698:0.348868:0.602223:0.348868:0.000000
:@0.603937:0.365713:0.610353:0.365713:0.610353:0.349895:0.603937:0.349895:0.000000
F:@0.630523:0.365337:0.638075:0.365337:0.638075:0.348868:0.630523:0.348868:0.000000
:@0.632700:0.363197:0.639116:0.363197:0.639116:0.347379:0.632700:0.347379:0.000000
2:@0.637572:0.368498:0.642525:0.368498:0.642525:0.358880:0.637572:0.358880:0.000000
ha elegido como 2 .:@0.404234:0.382572:0.547546:0.382572:0.547546:0.366074:0.404234:0.366074:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.535814:0.382688:0.544791:0.382688:0.544791:0.366219:0.535814:0.366219:0.000000
De la definición de hipérbola, esto es, del conjunto  (0,  ,  ), se tie-:@0.404234:0.412748:0.891755:0.412747:0.891755:0.396250:0.404234:0.396250:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℋ:@0.772678:0.419821:0.789090:0.419821:0.789090:0.401686:0.772678:0.401686:0.000000
:@0.796315:0.410723:0.802730:0.410723:0.802730:0.394905:0.796315:0.394905:0.000000
a b:@0.810032:0.412863:0.835674:0.412863:0.835674:0.396394:0.810032:0.396394:0.000000:0.000000:0.000000
nen las siguientes equivalencias: :@0.404229:0.430098:0.632501:0.430098:0.632501:0.413600:0.404229:0.413600:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.404229:0.460390:0.411704:0.460390:0.411704:0.443921:0.404229:0.443921:0.000000
:@0.405924:0.460766:0.412339:0.460766:0.412339:0.444948:0.405924:0.444948:0.000000
    (0,  ,  ) :@0.412339:0.460274:0.506602:0.460273:0.506602:0.443776:0.412339:0.443776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.415718:0.459755:0.430371:0.459755:0.430371:0.446381:0.415718:0.446381:0.000000
ℋ:@0.434511:0.467347:0.450923:0.467347:0.450923:0.449212:0.434511:0.449212:0.000000
:@0.458150:0.458249:0.464565:0.458249:0.464565:0.442431:0.458150:0.442431:0.000000
a b:@0.471366:0.460389:0.496507:0.460389:0.496507:0.443920:0.471366:0.443920:0.000000:0.000000:0.000000
 :@0.522453:0.460321:0.526359:0.460321:0.526359:0.444333:0.522453:0.444333:0.000000
| ||  –  || – ||  –  || | = 2 ,:@0.526359:0.460273:0.720592:0.460273:0.720592:0.443776:0.526359:0.443776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.545528:0.460389:0.553003:0.460389:0.553003:0.443920:0.545528:0.443920:0.000000
:@0.547224:0.460765:0.553639:0.460765:0.553639:0.444947:0.547224:0.444947:0.000000
F:@0.572423:0.460389:0.579975:0.460389:0.579975:0.443920:0.572423:0.443920:0.000000
:@0.574580:0.458249:0.580996:0.458249:0.580996:0.442431:0.574580:0.442431:0.000000
1:@0.579453:0.463550:0.584406:0.463550:0.584406:0.453932:0.579453:0.453932:0.000000
x:@0.623226:0.460389:0.630701:0.460389:0.630701:0.443920:0.623226:0.443920:0.000000
:@0.624921:0.460765:0.631337:0.460765:0.631337:0.444947:0.624921:0.444947:0.000000
F:@0.650120:0.460389:0.657672:0.460389:0.657672:0.443920:0.650120:0.443920:0.000000
:@0.652278:0.458249:0.658693:0.458249:0.658693:0.442431:0.652278:0.442431:0.000000
2:@0.657150:0.463550:0.662104:0.463550:0.662104:0.453932:0.657150:0.453932:0.000000
a:@0.708859:0.460389:0.717837:0.460389:0.717837:0.443920:0.708859:0.443920:0.000000
x:@0.404237:0.477740:0.411712:0.477740:0.411712:0.461271:0.404237:0.461271:0.000000
:@0.405932:0.478116:0.412348:0.478116:0.412348:0.462298:0.405932:0.462298:0.000000
    (0,  ,  )   | ||  –  || – ||  –  || | ≠ 2 .:@0.412348:0.477624:0.720828:0.477624:0.720828:0.461126:0.412348:0.461126:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.415718:0.477105:0.430371:0.477105:0.430371:0.463732:0.415718:0.463732:0.000000
ℋ:@0.434511:0.484698:0.450923:0.484698:0.450923:0.466563:0.434511:0.466563:0.000000
:@0.458150:0.475600:0.464565:0.475600:0.464565:0.459782:0.458150:0.459782:0.000000
a b:@0.471366:0.477740:0.496507:0.477740:0.496507:0.461271:0.471366:0.461271:0.000000:0.000000:0.000000
x:@0.545764:0.477740:0.553239:0.477740:0.553239:0.461271:0.545764:0.461271:0.000000
:@0.547459:0.478116:0.553874:0.478116:0.553874:0.462298:0.547459:0.462298:0.000000
F:@0.572658:0.477740:0.580210:0.477740:0.580210:0.461271:0.572658:0.461271:0.000000
:@0.574816:0.475600:0.581231:0.475600:0.581231:0.459782:0.574816:0.459782:0.000000
1:@0.579689:0.480901:0.584642:0.480901:0.584642:0.471283:0.579689:0.471283:0.000000
x:@0.623461:0.477740:0.630935:0.477740:0.630935:0.461271:0.623461:0.461271:0.000000
:@0.625156:0.478116:0.631571:0.478116:0.631571:0.462298:0.625156:0.462298:0.000000
F:@0.650355:0.477740:0.657907:0.477740:0.657907:0.461271:0.650355:0.461271:0.000000
:@0.652513:0.475600:0.658928:0.475600:0.658928:0.459782:0.652513:0.459782:0.000000
2:@0.657385:0.480901:0.662338:0.480901:0.662338:0.471283:0.657385:0.471283:0.000000
a:@0.709095:0.477740:0.718073:0.477740:0.718073:0.461271:0.709095:0.461271:0.000000
Sea   = ( ,  )    . La distancia de   a   está definida como::@0.404242:0.507800:0.829728:0.507799:0.829728:0.491302:0.404242:0.491302:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.432504:0.507916:0.439979:0.507916:0.439979:0.491447:0.432504:0.491447:0.000000
:@0.434200:0.508292:0.440615:0.508292:0.440615:0.492473:0.434200:0.492473:0.000000
x y:@0.464889:0.507916:0.486948:0.507916:0.486948:0.491447:0.464889:0.491447:0.000000:0.000000:0.000000
:@0.497034:0.507281:0.511687:0.507281:0.511687:0.493907:0.497034:0.493907:0.000000
:@0.515829:0.506712:0.529134:0.506712:0.529134:0.493850:0.515829:0.493850:0.000000
2:@0.529134:0.501446:0.534087:0.501446:0.534087:0.491828:0.529134:0.491828:0.000000
x F:@0.650099:0.507915:0.681889:0.507915:0.681889:0.491446:0.650099:0.491446:0.000000:0.000000:0.000000
:@0.651796:0.508291:0.658212:0.508291:0.658212:0.492473:0.651796:0.492473:0.000000
:@0.676494:0.505775:0.682910:0.505775:0.682910:0.489957:0.676494:0.489957:0.000000
1:@0.681366:0.511076:0.686319:0.511076:0.686319:0.501458:0.681366:0.501458:0.000000
||  –  || =    (  +  )  +   , y la distancia de   a   es:@0.404238:0.532278:0.759296:0.532278:0.759296:0.515780:0.404238:0.515781:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.414256:0.532394:0.421731:0.532394:0.421731:0.515925:0.414256:0.515925:0.000000
:@0.415951:0.532770:0.422366:0.532770:0.422366:0.516952:0.415951:0.516952:0.000000
F:@0.441150:0.532394:0.448702:0.532394:0.448702:0.515925:0.441150:0.515925:0.000000
:@0.443308:0.530254:0.449723:0.530254:0.449723:0.514436:0.443308:0.514436:0.000000
1:@0.448179:0.535554:0.453133:0.535554:0.453133:0.525936:0.448179:0.525936:0.000000
x c:@0.500620:0.532393:0.534373:0.532393:0.534373:0.515925:0.500620:0.515925:0.000000:0.000000:0.000000
2:@0.540324:0.525925:0.545277:0.525925:0.545277:0.516307:0.540324:0.516307:0.000000
y:@0.564370:0.532393:0.572057:0.532393:0.572057:0.515925:0.564370:0.515925:0.000000
2:@0.572055:0.525925:0.577008:0.525925:0.577008:0.516307:0.572055:0.516307:0.000000
x F:@0.704562:0.532393:0.736352:0.532393:0.736352:0.515925:0.704562:0.515925:0.000000:0.000000:0.000000
:@0.706259:0.532769:0.712675:0.532769:0.712675:0.516951:0.706259:0.516951:0.000000
:@0.730957:0.530253:0.737373:0.530253:0.737373:0.514435:0.730957:0.514435:0.000000
2:@0.735828:0.535554:0.740781:0.535554:0.740781:0.525936:0.735828:0.525936:0.000000
||  –  || =    (  +  )  +   . Primeramente  (0,  ,  ) ≠ 0,:@0.404237:0.556757:0.791756:0.556756:0.791756:0.540258:0.404237:0.540259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.414255:0.556872:0.421730:0.556872:0.421730:0.540404:0.414255:0.540404:0.000000
:@0.415950:0.557248:0.422366:0.557248:0.422366:0.541430:0.415950:0.541430:0.000000
F:@0.441149:0.556872:0.448701:0.556872:0.448701:0.540404:0.441149:0.540404:0.000000
:@0.443307:0.554733:0.449722:0.554733:0.449722:0.538914:0.443307:0.538914:0.000000
2:@0.448179:0.560034:0.453133:0.560034:0.453133:0.550416:0.448179:0.550416:0.000000
x c:@0.500620:0.556872:0.534373:0.556872:0.534373:0.540403:0.500620:0.540403:0.000000:0.000000:0.000000
2:@0.540324:0.550404:0.545277:0.550404:0.545277:0.540786:0.540324:0.540786:0.000000
y:@0.564370:0.556872:0.572057:0.556872:0.572057:0.540403:0.564370:0.540403:0.000000
2:@0.572055:0.550404:0.577008:0.550404:0.577008:0.540786:0.572055:0.540786:0.000000
ℋ:@0.693466:0.563830:0.709878:0.563830:0.709878:0.545695:0.693466:0.545695:0.000000
:@0.717103:0.554732:0.723518:0.554732:0.723518:0.538914:0.717103:0.538914:0.000000
a b:@0.730319:0.556872:0.755460:0.556872:0.755460:0.540403:0.730319:0.540403:0.000000:0.000000:0.000000
pues 0    (0,  ,  ). En efecto, ||0 –  || =  , ||0 –  || =  , luego,:@0.404235:0.581235:0.847229:0.581235:0.847229:0.564737:0.404235:0.564737:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.443363:0.579211:0.449778:0.579211:0.449778:0.563393:0.443363:0.563393:0.000000
:@0.453823:0.580716:0.468476:0.580716:0.468476:0.567343:0.453823:0.567343:0.000000
ℋ:@0.472617:0.589333:0.490591:0.589333:0.490591:0.569471:0.472617:0.569471:0.000000
:@0.497816:0.579210:0.504231:0.579210:0.504231:0.563392:0.497816:0.563392:0.000000
a b:@0.511032:0.581350:0.536173:0.581350:0.536173:0.564881:0.511032:0.564881:0.000000:0.000000:0.000000
:@0.633482:0.579210:0.639897:0.579210:0.639897:0.563392:0.633482:0.563392:0.000000
F:@0.658584:0.581350:0.666136:0.581350:0.666136:0.564881:0.658584:0.564881:0.000000
:@0.660742:0.579210:0.667158:0.579210:0.667158:0.563392:0.660742:0.563392:0.000000
1:@0.665615:0.584512:0.670569:0.584512:0.670569:0.574894:0.665615:0.574894:0.000000
c:@0.699677:0.581350:0.706863:0.581350:0.706863:0.564881:0.699677:0.564881:0.000000
:@0.725050:0.579210:0.731465:0.579210:0.731465:0.563392:0.725050:0.563392:0.000000
F:@0.750152:0.581350:0.757704:0.581350:0.757704:0.564881:0.750152:0.564881:0.000000
:@0.752310:0.579210:0.758725:0.579210:0.758725:0.563392:0.752310:0.563392:0.000000
2:@0.757182:0.584512:0.762136:0.584512:0.762136:0.574894:0.757182:0.574894:0.000000
c:@0.791246:0.581350:0.798432:0.581350:0.798432:0.564881:0.791246:0.564881:0.000000
||0 –  || – ||0 –  || = 0 < 2 , lo que demuestra que 0    (0,  ,  ).:@0.404245:0.605714:0.873719:0.605714:0.873719:0.589217:0.404245:0.589216:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.415535:0.603689:0.421950:0.603689:0.421950:0.587871:0.415535:0.587871:0.000000
F:@0.440637:0.605829:0.448189:0.605829:0.448189:0.589360:0.440637:0.589360:0.000000
:@0.442795:0.603689:0.449211:0.603689:0.449211:0.587871:0.442795:0.587871:0.000000
1:@0.447658:0.608991:0.452612:0.608991:0.452612:0.599373:0.447658:0.599373:0.000000
:@0.492703:0.603690:0.499118:0.603690:0.499118:0.587872:0.492703:0.587872:0.000000
F:@0.517806:0.605830:0.525358:0.605830:0.525358:0.589361:0.517806:0.589361:0.000000
:@0.519963:0.603690:0.526379:0.603690:0.526379:0.587872:0.519963:0.587872:0.000000
2:@0.524837:0.608991:0.529790:0.608991:0.529790:0.599373:0.524837:0.599373:0.000000
a:@0.594982:0.605830:0.603960:0.605830:0.603960:0.589361:0.594982:0.589361:0.000000
:@0.772203:0.603690:0.778619:0.603690:0.778619:0.587872:0.772203:0.587872:0.000000
:@0.782659:0.605196:0.797312:0.605196:0.797312:0.591822:0.782659:0.591822:0.000000
ℋ:@0.801455:0.613813:0.819429:0.613813:0.819429:0.593950:0.801455:0.593950:0.000000
:@0.826654:0.603690:0.833069:0.603690:0.833069:0.587872:0.826654:0.587872:0.000000
a b:@0.839870:0.605830:0.865011:0.605830:0.865011:0.589361:0.839870:0.589361:0.000000:0.000000:0.000000
Por otro lado, de la propiedad de la norma siguiente::@0.404244:0.630193:0.775713:0.630193:0.775713:0.613696:0.404244:0.613696:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
| || || – || || | ≤ ||  –  ||    :@0.404244:0.647544:0.589518:0.647544:0.589518:0.631046:0.404244:0.631046:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.423413:0.647660:0.430888:0.647660:0.430888:0.631191:0.423413:0.631191:0.000000
:@0.425108:0.648036:0.431523:0.648036:0.431523:0.632217:0.425108:0.632217:0.000000
y:@0.471113:0.647660:0.478800:0.647660:0.478800:0.631191:0.471113:0.631191:0.000000
:@0.472250:0.648036:0.478665:0.648036:0.478665:0.632217:0.472250:0.632217:0.000000
x:@0.527715:0.647660:0.535190:0.647660:0.535190:0.631191:0.527715:0.631191:0.000000
:@0.529410:0.648036:0.535825:0.648036:0.535825:0.632217:0.529410:0.632217:0.000000
y:@0.554609:0.647660:0.562296:0.647660:0.562296:0.631191:0.554609:0.631191:0.000000
:@0.555746:0.648036:0.562161:0.648036:0.562161:0.632217:0.555746:0.632217:0.000000
∀:@0.589506:0.655130:0.601079:0.655130:0.601079:0.636131:0.589506:0.636131:0.000000
x y:@0.601085:0.647659:0.623780:0.647659:0.623780:0.631190:0.601085:0.631190:0.000000:0.000000:0.000000
  :@0.602781:0.648035:0.629232:0.648035:0.629232:0.632217:0.602781:0.632217:0.000000:0.000000:0.000000:0.000000
, :@0.609196:0.647543:0.616093:0.647543:0.616093:0.631046:0.609196:0.631046:0.000000:0.000000
:@0.629231:0.647025:0.643883:0.647025:0.643883:0.633651:0.629231:0.633651:0.000000
  , así::@0.643883:0.647543:0.693986:0.647543:0.693986:0.631046:0.643883:0.631046:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.648025:0.646456:0.661330:0.646456:0.661330:0.633594:0.648025:0.633594:0.000000
2:@0.661330:0.641192:0.666283:0.641192:0.666283:0.631573:0.661330:0.631573:0.000000
2  = | ||  –  || – ||  –  || | = | ||  –  || – ||  –  || | ≤ ||  –  || = 2 ,:@0.404236:0.682245:0.889126:0.682245:0.889126:0.665747:0.404236:0.665747:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.412732:0.682361:0.421710:0.682361:0.421710:0.665892:0.412732:0.665892:0.000000
x:@0.459971:0.682361:0.467445:0.682361:0.467445:0.665892:0.459971:0.665892:0.000000
:@0.461666:0.682736:0.468081:0.682736:0.468081:0.666918:0.461666:0.666918:0.000000
F:@0.486865:0.682361:0.494417:0.682361:0.494417:0.665892:0.486865:0.665892:0.000000
:@0.489023:0.680221:0.495438:0.680221:0.495438:0.664402:0.489023:0.664402:0.000000
1:@0.493895:0.685523:0.498848:0.685523:0.498848:0.675905:0.493895:0.675905:0.000000
x:@0.537667:0.682361:0.545141:0.682361:0.545141:0.665892:0.537667:0.665892:0.000000
:@0.539362:0.682736:0.545777:0.682736:0.545777:0.666918:0.539362:0.666918:0.000000
F:@0.564561:0.682361:0.572113:0.682361:0.572113:0.665892:0.564561:0.665892:0.000000
:@0.566719:0.680221:0.573134:0.680221:0.573134:0.664402:0.566719:0.664402:0.000000
2:@0.571591:0.685523:0.576544:0.685523:0.576544:0.675905:0.571591:0.675905:0.000000
F:@0.633974:0.682361:0.641526:0.682361:0.641526:0.665892:0.633974:0.665892:0.000000
:@0.636132:0.680221:0.642547:0.680221:0.642547:0.664402:0.636132:0.664402:0.000000
1:@0.641005:0.685523:0.645958:0.685523:0.645958:0.675905:0.641005:0.675905:0.000000
x:@0.664742:0.682361:0.672217:0.682361:0.672217:0.665892:0.664742:0.665892:0.000000
:@0.666437:0.682736:0.672852:0.682736:0.672852:0.666918:0.666437:0.666918:0.000000
x:@0.711672:0.682361:0.719147:0.682361:0.719147:0.665892:0.711672:0.665892:0.000000
:@0.713367:0.682736:0.719783:0.682736:0.719783:0.666918:0.713367:0.666918:0.000000
F:@0.738566:0.682361:0.746118:0.682361:0.746118:0.665892:0.738566:0.665892:0.000000
:@0.740724:0.680221:0.747139:0.680221:0.747139:0.664402:0.740724:0.664402:0.000000
2:@0.745596:0.685523:0.750550:0.685523:0.750550:0.675905:0.745596:0.675905:0.000000
F:@0.798827:0.682361:0.806379:0.682361:0.806379:0.665892:0.798827:0.665892:0.000000
:@0.800985:0.680221:0.807400:0.680221:0.807400:0.664402:0.800985:0.664402:0.000000
1:@0.805858:0.685523:0.810811:0.685523:0.810811:0.675905:0.805858:0.675905:0.000000
F:@0.829595:0.682361:0.837147:0.682361:0.837147:0.665892:0.829595:0.665892:0.000000
:@0.831753:0.680221:0.838168:0.680221:0.838168:0.664402:0.831753:0.664402:0.000000
2:@0.836626:0.685523:0.841579:0.685523:0.841579:0.675905:0.836626:0.675905:0.000000
c:@0.879185:0.682361:0.886371:0.682361:0.886371:0.665892:0.879185:0.665892:0.000000
 :@0.404239:0.699596:0.408381:0.699596:0.408381:0.683098:0.404239:0.683098:0.000000
con lo que si      (0,  ,  ), resulta::@0.404239:0.716946:0.655888:0.716946:0.655888:0.700449:0.404239:0.700449:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.498272:0.717062:0.505747:0.717062:0.505747:0.700593:0.498272:0.700593:0.000000
:@0.499968:0.717438:0.506383:0.717438:0.506383:0.701620:0.499968:0.701620:0.000000
:@0.510520:0.716428:0.525173:0.716428:0.525173:0.703054:0.510520:0.703054:0.000000
ℋ:@0.529315:0.725045:0.547290:0.725045:0.547290:0.705183:0.529315:0.705183:0.000000
:@0.554514:0.714922:0.560930:0.714922:0.560930:0.699104:0.554514:0.699104:0.000000
a b:@0.567730:0.717062:0.592872:0.717062:0.592872:0.700593:0.567730:0.700593:0.000000:0.000000:0.000000
2  = | ||  –  || – ||  –  || | ≤ ||  –  ||.:@0.404226:0.751648:0.680348:0.751648:0.680348:0.735150:0.404226:0.735150:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.412722:0.751764:0.421700:0.751764:0.421700:0.735295:0.412722:0.735295:0.000000
x:@0.459961:0.751764:0.467435:0.751764:0.467435:0.735295:0.459961:0.735295:0.000000
:@0.461656:0.752139:0.468071:0.752139:0.468071:0.736321:0.461656:0.736321:0.000000
F:@0.486855:0.751764:0.494407:0.751764:0.494407:0.735295:0.486855:0.735295:0.000000
:@0.489013:0.749624:0.495428:0.749624:0.495428:0.733805:0.489013:0.733805:0.000000
1:@0.493895:0.754926:0.498848:0.754926:0.498848:0.745308:0.493895:0.745308:0.000000
x:@0.537667:0.751764:0.545141:0.751764:0.545141:0.735295:0.537667:0.735295:0.000000
:@0.539362:0.752139:0.545777:0.752139:0.545777:0.736321:0.539362:0.736321:0.000000
F:@0.564561:0.751764:0.572113:0.751764:0.572113:0.735295:0.564561:0.735295:0.000000
:@0.566719:0.749624:0.573134:0.749624:0.573134:0.733805:0.566719:0.733805:0.000000
2:@0.571591:0.754926:0.576544:0.754926:0.576544:0.745308:0.571591:0.745308:0.000000
F:@0.624823:0.751764:0.632375:0.751764:0.632375:0.735295:0.624823:0.735295:0.000000
:@0.626981:0.749624:0.633396:0.749624:0.633396:0.733805:0.626981:0.733805:0.000000
1:@0.631854:0.754926:0.636808:0.754926:0.636808:0.745308:0.631854:0.745308:0.000000
F:@0.655590:0.751764:0.663142:0.751764:0.663142:0.735295:0.655590:0.735295:0.000000
:@0.657748:0.749624:0.664163:0.749624:0.664163:0.733805:0.657748:0.733805:0.000000
2:@0.662622:0.754926:0.667575:0.754926:0.667575:0.745308:0.662622:0.745308:0.000000
En la Figura 2.35. se muestran los focos  ,   y un punto:@0.404239:0.786349:0.795723:0.786349:0.795723:0.769852:0.404239:0.769852:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F F:@0.681136:0.786465:0.707563:0.786465:0.707563:0.769996:0.681136:0.769996:0.000000:0.000000:0.000000
 :@0.683296:0.784325:0.708585:0.784325:0.708585:0.768507:0.683296:0.768507:0.000000:0.000000:0.000000
1:@0.688163:0.789627:0.693116:0.789627:0.693116:0.780009:0.688163:0.780009:0.000000
2:@0.707044:0.789627:0.711997:0.789627:0.711997:0.780009:0.707044:0.780009:0.000000
x:@0.404234:0.803816:0.411709:0.803816:0.411709:0.787347:0.404234:0.787347:0.000000
:@0.405929:0.804192:0.412344:0.804192:0.412344:0.788374:0.405929:0.788374:0.000000
 = (x,y)     que pertenece a la hipérbola  (0,  ,  ). :@0.412344:0.803700:0.792723:0.803700:0.792723:0.787202:0.412344:0.787202:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.468465:0.803181:0.483117:0.803181:0.483117:0.789808:0.468465:0.789808:0.000000
:@0.487259:0.802613:0.500564:0.802613:0.500564:0.789751:0.487259:0.789751:0.000000
2:@0.500562:0.797348:0.505516:0.797348:0.505516:0.787730:0.500562:0.787730:0.000000
ℋ:@0.716313:0.811799:0.734287:0.811799:0.734287:0.791936:0.716313:0.791936:0.000000
:@0.741516:0.801676:0.747931:0.801676:0.747931:0.785858:0.741516:0.785858:0.000000
a b:@0.754732:0.803816:0.779873:0.803816:0.779873:0.787347:0.754732:0.787347:0.000000:0.000000:0.000000
Obtengamos la ecuación cartesiana de la hipérbola. De la definición :@0.404239:0.836898:0.895940:0.836898:0.895940:0.820400:0.404239:0.820400:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del conjunto  (0,  ,  ) se sigue que::@0.404239:0.854249:0.661488:0.854249:0.661488:0.837751:0.404239:0.837751:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℋ:@0.499371:0.862348:0.517345:0.862348:0.517345:0.842485:0.499371:0.842485:0.000000
:@0.524569:0.852224:0.530985:0.852224:0.530985:0.836406:0.524569:0.836406:0.000000
a b:@0.537785:0.854364:0.562927:0.854364:0.562927:0.837896:0.537785:0.837896:0.000000:0.000000:0.000000
x:@0.404239:0.887562:0.411714:0.887562:0.411714:0.871093:0.404239:0.871093:0.000000
:@0.405934:0.887938:0.412349:0.887938:0.412349:0.872120:0.405934:0.872120:0.000000
 = ( ,  )    (0,  ,  )   | ||  –  || – ||  –  || | = 2:@0.412349:0.887446:0.762150:0.887436:0.762150:0.870939:0.412349:0.870949:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.436624:0.887562:0.458682:0.887562:0.458682:0.871093:0.436624:0.871093:0.000000:0.000000:0.000000
:@0.468773:0.886918:0.483426:0.886918:0.483426:0.873544:0.468773:0.873544:0.000000
ℋ:@0.487566:0.894510:0.503977:0.894510:0.503977:0.876375:0.487566:0.876375:0.000000
:@0.511204:0.885412:0.517620:0.885412:0.517620:0.869594:0.511204:0.869594:0.000000
a b:@0.524420:0.887552:0.549562:0.887552:0.549562:0.871083:0.524420:0.871083:0.000000:0.000000:0.000000
x:@0.598819:0.887552:0.606294:0.887552:0.606294:0.871083:0.598819:0.871083:0.000000
:@0.600514:0.887928:0.606929:0.887928:0.606929:0.872110:0.600514:0.872110:0.000000
F:@0.625713:0.887552:0.633265:0.887552:0.633265:0.871083:0.625713:0.871083:0.000000
:@0.627871:0.885412:0.634286:0.885412:0.634286:0.869594:0.627871:0.869594:0.000000
1:@0.632744:0.890714:0.637697:0.890714:0.637697:0.881096:0.632744:0.881096:0.000000
x:@0.676515:0.887552:0.683990:0.887552:0.683990:0.871083:0.676515:0.871083:0.000000
:@0.678211:0.887928:0.684626:0.887928:0.684626:0.872110:0.678211:0.872110:0.000000
F:@0.703410:0.887552:0.710962:0.887552:0.710962:0.871083:0.703410:0.871083:0.000000
:@0.705567:0.885412:0.711983:0.885412:0.711983:0.869594:0.705567:0.869594:0.000000
2:@0.710440:0.890714:0.715393:0.890714:0.715393:0.881096:0.710440:0.881096:0.000000
a:@0.762150:0.887552:0.771128:0.887552:0.771128:0.871083:0.762150:0.871083:0.000000
     (  +  )  +   –   (  –  )  + :@0.420089:0.911915:0.620469:0.911915:0.620469:0.895417:0.420089:0.895417:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
|:@0.424230:0.912652:0.429239:0.912652:0.429239:0.892855:0.424230:0.892855:0.000000
x c:@0.447618:0.912030:0.481371:0.912030:0.481371:0.895562:0.447618:0.895562:0.000000:0.000000:0.000000
2:@0.487323:0.905563:0.492276:0.905563:0.492276:0.895945:0.487323:0.895945:0.000000
y:@0.511367:0.912030:0.519054:0.912030:0.519054:0.895562:0.511367:0.895562:0.000000
2:@0.519054:0.905563:0.524007:0.905563:0.524007:0.895945:0.519054:0.895945:0.000000
x c:@0.557028:0.912030:0.590473:0.912030:0.590473:0.895562:0.557028:0.895562:0.000000:0.000000:0.000000
2:@0.596423:0.905563:0.601376:0.905563:0.601376:0.895945:0.596423:0.895945:0.000000
y:@0.620469:0.912030:0.628155:0.912030:0.628155:0.895562:0.620469:0.895562:0.000000
2  :@0.628155:0.905563:0.638500:0.905563:0.638500:0.895945:0.628155:0.895945:0.000000:0.000000:0.000000
|:@0.638498:0.912652:0.643507:0.912652:0.643507:0.892855:0.638498:0.892855:0.000000
 = 2:@0.643507:0.911915:0.671095:0.911915:0.671095:0.895417:0.643507:0.895417:0.000000:0.000000:0.000000:0.000000
a.:@0.671095:0.912030:0.682616:0.912030:0.682616:0.895562:0.671095:0.895562:0.000000:0.000000
p:@0.143988:0.913915:0.155468:0.913915:0.155468:0.903891:0.143988:0.903891:0.000000
 :@0.155468:0.914623:0.158350:0.914623:0.158350:0.903146:0.155468:0.903146:0.000000
Figura 2.35.:@0.158350:0.914623:0.212828:0.914623:0.212828:0.903146:0.158350:0.903146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.199646:0.097890:0.307805:0.097890:0.307805:0.082418:0.199646:0.082418:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué es una hipérbola?:@0.199884:0.126518:0.350296:0.126518:0.350296:0.111455:0.199884:0.111455:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.173669:0.363493:0.173669:0.363493:0.158197:0.199646:0.158197:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué importancia :@0.199884:0.202297:0.321167:0.202297:0.321167:0.187233:0.199884:0.187233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tienen los dos puntos fijos :@0.153341:0.218139:0.327058:0.218139:0.327058:0.203075:0.153341:0.203075:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
llamados focos para el cálculo :@0.153341:0.233981:0.350345:0.233981:0.350345:0.218917:0.153341:0.218917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la ecuación cartesiana de la :@0.153341:0.249823:0.353425:0.249823:0.353425:0.234759:0.153341:0.234759:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hipérbola?:@0.153341:0.265665:0.220709:0.265665:0.220709:0.250601:0.153341:0.250601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.267371:0.858843:0.272055:0.858843:0.272055:0.850251:0.267371:0.850251:0.000000
0:@0.250181:0.849309:0.254614:0.849309:0.254614:0.840702:0.250181:0.840702:0.000000
y:@0.240748:0.787686:0.247209:0.787686:0.247209:0.774057:0.240748:0.774057:0.000000
x:@0.357594:0.855375:0.364199:0.855375:0.364199:0.841746:0.357594:0.841746:0.000000
b:@0.248007:0.828965:0.252841:0.828965:0.252841:0.820373:0.248007:0.820373:0.000000
c:@0.286584:0.840085:0.290333:0.840085:0.290333:0.831492:0.286584:0.831492:0.000000
–a:@0.225813:0.845848:0.235734:0.845848:0.235734:0.837256:0.225813:0.837256:0.000000:0.000000
–c:@0.211510:0.840085:0.220496:0.840085:0.220496:0.831492:0.211510:0.831492:0.000000:0.000000
–b:@0.242770:0.860400:0.252841:0.860400:0.252841:0.851808:0.242770:0.851808:0.000000:0.000000
F:@0.287464:0.851920:0.292389:0.851920:0.292389:0.841180:0.287464:0.841180:0.000000
:@0.288871:0.850911:0.293055:0.850911:0.293055:0.840595:0.288871:0.840595:0.000000
1:@0.291734:0.852725:0.294964:0.852725:0.294964:0.846453:0.291734:0.846453:0.000000
F:@0.212078:0.851920:0.217003:0.851920:0.217003:0.841180:0.212078:0.841180:0.000000
:@0.213485:0.850911:0.217669:0.850911:0.217669:0.840595:0.213485:0.840595:0.000000
2:@0.216348:0.852725:0.219578:0.852725:0.219578:0.846453:0.216348:0.846453:0.000000
x:@0.306483:0.824379:0.311358:0.824379:0.311358:0.813638:0.306483:0.813638:0.000000
:@0.307588:0.824624:0.311772:0.824624:0.311772:0.814308:0.307588:0.814308:0.000000
x:@0.297964:0.839071:0.302839:0.839071:0.302839:0.828330:0.297964:0.828330:0.000000
:@0.299070:0.839316:0.303254:0.839316:0.303254:0.829000:0.299070:0.829000:0.000000
 – :@0.303254:0.838995:0.315504:0.838995:0.315504:0.828236:0.303254:0.828236:0.000000:0.000000:0.000000
F:@0.315504:0.839071:0.320429:0.839071:0.320429:0.828330:0.315504:0.828330:0.000000
:@0.316911:0.838062:0.321095:0.838062:0.321095:0.827745:0.316911:0.827745:0.000000
1:@0.319779:0.839875:0.323009:0.839875:0.323009:0.833602:0.319779:0.833602:0.000000
x:@0.259854:0.817538:0.264729:0.817538:0.264729:0.806797:0.259854:0.806797:0.000000
:@0.260960:0.817783:0.265144:0.817783:0.265144:0.807467:0.260960:0.807467:0.000000
 – :@0.265144:0.817463:0.277394:0.817463:0.277394:0.806703:0.265144:0.806703:0.000000:0.000000:0.000000
F:@0.277394:0.817538:0.282319:0.817538:0.282319:0.806797:0.277394:0.806797:0.000000
:@0.278801:0.816529:0.282985:0.816529:0.282985:0.806213:0.278801:0.806213:0.000000
2:@0.281666:0.818342:0.284896:0.818342:0.284896:0.812069:0.281666:0.812069:0.000000
Competencia :@0.199785:0.403618:0.297408:0.403618:0.297408:0.388146:0.199785:0.388146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comunicacional:@0.199785:0.416186:0.311744:0.416186:0.311744:0.400714:0.199785:0.400714:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aprende la definición de :@0.193213:0.440659:0.357361:0.440659:0.357361:0.425596:0.193213:0.425596:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la exentricidad de la hipérbola::@0.153477:0.456501:0.351221:0.456501:0.351221:0.441438:0.153477:0.441438:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean :@0.153477:0.479789:0.187989:0.479789:0.187989:0.464726:0.153477:0.464726:0.000000:0.000000:0.000000:0.000000:0.000000
a b c:@0.187996:0.479957:0.223438:0.479957:0.223438:0.464624:0.187996:0.464624:0.000000:0.000000:0.000000:0.000000:0.000000
,  ,     :@0.196175:0.479849:0.244269:0.479849:0.244269:0.464490:0.196175:0.464490:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.226934:0.479366:0.240575:0.479366:0.240575:0.466916:0.226934:0.466916:0.000000
:@0.244088:0.478837:0.256475:0.478837:0.256475:0.466863:0.244088:0.466863:0.000000
2:@0.256304:0.473935:0.260916:0.473935:0.260916:0.464981:0.256304:0.464981:0.000000
, tal que :@0.260811:0.479783:0.315410:0.479783:0.315410:0.464720:0.260811:0.464720:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0 <   <   y   =   –  , :@0.153494:0.495942:0.303117:0.495937:0.303117:0.480874:0.153494:0.480879:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a c:@0.178674:0.496111:0.210975:0.496111:0.210975:0.480778:0.178674:0.480778:0.000000:0.000000:0.000000
b:@0.225500:0.496042:0.233961:0.496042:0.233961:0.481006:0.225500:0.481006:0.000000
2:@0.233960:0.490089:0.238571:0.490089:0.238571:0.481135:0.233960:0.481135:0.000000
c:@0.255898:0.496042:0.262459:0.496042:0.262459:0.481006:0.255898:0.481006:0.000000
2:@0.262459:0.490089:0.267070:0.490089:0.267070:0.481135:0.262459:0.481135:0.000000
a:@0.284116:0.496042:0.292313:0.496042:0.292313:0.481006:0.284116:0.481006:0.000000
2:@0.292312:0.490089:0.296923:0.490089:0.296923:0.481135:0.292312:0.481135:0.000000
F:@0.153486:0.511884:0.160381:0.511884:0.160381:0.496848:0.153486:0.496848:0.000000
:@0.155456:0.509930:0.161314:0.509930:0.161314:0.495488:0.155456:0.495488:0.000000
1:@0.159906:0.514772:0.164428:0.514772:0.164428:0.505990:0.159906:0.505990:0.000000
 = (–  , 0),   = (  , 0), los focos :@0.164427:0.511779:0.360870:0.511779:0.360870:0.496716:0.164427:0.496716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.196353:0.511884:0.202914:0.511884:0.202914:0.496848:0.196353:0.496848:0.000000
F:@0.231603:0.511884:0.238498:0.511884:0.238498:0.496848:0.231603:0.496848:0.000000
:@0.233573:0.509930:0.239430:0.509930:0.239430:0.495488:0.233573:0.495488:0.000000
2:@0.238022:0.514772:0.242544:0.514772:0.242544:0.505990:0.238022:0.505990:0.000000
c:@0.265411:0.511884:0.271972:0.511884:0.271972:0.496848:0.265411:0.496848:0.000000
de la hipérbola  (0,  ,  ).:@0.153485:0.527621:0.318490:0.527621:0.318490:0.512558:0.153485:0.512558:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℋ:@0.253940:0.534079:0.268924:0.534079:0.268924:0.517521:0.253940:0.517521:0.000000
:@0.275521:0.525772:0.281378:0.525772:0.281378:0.511330:0.275521:0.511330:0.000000
a b:@0.287588:0.527726:0.310541:0.527726:0.310541:0.512690:0.287588:0.512690:0.000000:0.000000:0.000000
La excentricidad de la hipérbola :@0.153478:0.550592:0.363552:0.550592:0.363552:0.535528:0.153478:0.535528:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se define como:@0.153478:0.566434:0.253300:0.566434:0.253300:0.551370:0.153478:0.551370:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e:@0.200478:0.594395:0.207251:0.594395:0.207251:0.579358:0.200478:0.579358:0.000000
 =   = :@0.207251:0.594289:0.255132:0.594293:0.255132:0.579230:0.207251:0.579226:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.227917:0.586603:0.234478:0.586603:0.234478:0.571567:0.227917:0.571567:0.000000
a:@0.227108:0.601520:0.235305:0.601520:0.235305:0.586484:0.227108:0.586484:0.000000
 a:@0.260169:0.588419:0.272147:0.588419:0.272147:0.573383:0.260169:0.573383:0.000000:0.000000
2:@0.272147:0.582514:0.276669:0.582514:0.276669:0.573732:0.272147:0.573732:0.000000
 + :@0.276668:0.588313:0.294099:0.588313:0.294099:0.573251:0.276668:0.573251:0.000000:0.000000:0.000000
b:@0.294099:0.588419:0.302560:0.588419:0.302560:0.573383:0.294099:0.573383:0.000000
2:@0.302559:0.582514:0.307081:0.582514:0.307081:0.573732:0.302559:0.573732:0.000000
a:@0.279526:0.603342:0.287723:0.603342:0.287723:0.588305:0.279526:0.588305:0.000000
. :@0.312116:0.594293:0.318414:0.594293:0.318414:0.579230:0.312116:0.579230:0.000000:0.000000
Como   >   se tiene que:@0.153490:0.617264:0.314648:0.617264:0.314648:0.602201:0.153490:0.602201:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c a,:@0.198362:0.617369:0.232873:0.617369:0.232873:0.602333:0.198362:0.602333:0.000000:0.000000:0.000000:0.000000
e =   > 1.:@0.153490:0.645119:0.218997:0.645123:0.218997:0.630060:0.153490:0.630056:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.181510:0.637433:0.188070:0.637433:0.188070:0.622397:0.181510:0.622397:0.000000
a:@0.180701:0.652350:0.188897:0.652350:0.188897:0.637314:0.180701:0.637314:0.000000