99:@0.922460:0.966765:0.939432:0.966765:0.939432:0.950778:0.922460:0.950778:0.000000:0.000000
Asíntotas de la hipérbola:@0.108233:0.108020:0.309238:0.108020:0.309238:0.090337:0.108233:0.090337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De la ecuación cartesiana de la hipérbola:@0.108233:0.124727:0.398154:0.124727:0.398154:0.108230:0.108233:0.108230:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  )    , tal que         –         = 1,:@0.108233:0.149206:0.350690:0.149207:0.350690:0.132709:0.108233:0.132709:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.114186:0.149322:0.136245:0.149322:0.136245:0.132853:0.114186:0.132853:0.000000:0.000000:0.000000
:@0.146338:0.148688:0.160991:0.148688:0.160991:0.135315:0.146338:0.135315:0.000000
:@0.165133:0.148120:0.178437:0.148120:0.178437:0.135258:0.165133:0.135258:0.000000
2:@0.178437:0.142854:0.183391:0.142854:0.183391:0.133236:0.178437:0.133236:0.000000
se obtiene   =          1 –        ,   | | ≠ 0.:@0.108237:0.187046:0.383803:0.187051:0.383803:0.170553:0.108237:0.170548:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.185682:0.187162:0.193369:0.187162:0.193369:0.170693:0.185682:0.170693:0.000000
2:@0.193364:0.180698:0.198317:0.180698:0.198317:0.171079:0.193364:0.171079:0.000000
x:@0.242261:0.187166:0.249736:0.187166:0.249736:0.170697:0.242261:0.170697:0.000000
2:@0.249736:0.180698:0.254689:0.180698:0.254689:0.171079:0.249736:0.171079:0.000000
x:@0.340206:0.187166:0.347681:0.187166:0.347681:0.170697:0.340206:0.170697:0.000000
De este resultado, se obtienen dos ecuaciones cartesianas de rectas:@0.108233:0.221752:0.583863:0.221752:0.583863:0.205254:0.108233:0.205254:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  )     tal que   =       , :@0.226946:0.246230:0.421399:0.246230:0.421399:0.229733:0.226946:0.229733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.232899:0.246346:0.254957:0.246346:0.254957:0.229877:0.232899:0.229877:0.000000:0.000000:0.000000
:@0.265056:0.245712:0.279708:0.245712:0.279708:0.232339:0.265056:0.232339:0.000000
:@0.283850:0.245144:0.297155:0.245144:0.297155:0.232281:0.283850:0.232281:0.000000
2:@0.297155:0.239879:0.302108:0.239879:0.302108:0.230261:0.297155:0.230261:0.000000
y:@0.359538:0.246346:0.367225:0.246346:0.367225:0.229877:0.359538:0.229877:0.000000
x:@0.407027:0.246346:0.414502:0.246346:0.414502:0.229877:0.407027:0.229877:0.000000
( ,  )     tal que   = –      , :@0.226936:0.274267:0.431899:0.274273:0.431899:0.257776:0.226936:0.257769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.232888:0.274383:0.254947:0.274383:0.254947:0.257914:0.232888:0.257914:0.000000:0.000000:0.000000
:@0.265056:0.273755:0.279708:0.273755:0.279708:0.260381:0.265056:0.260381:0.000000
:@0.283850:0.273186:0.297155:0.273186:0.297155:0.260324:0.283850:0.260324:0.000000
2:@0.297155:0.267922:0.302108:0.267922:0.302108:0.258303:0.297155:0.258303:0.000000
y:@0.359538:0.274389:0.367225:0.274389:0.367225:0.257920:0.359538:0.257920:0.000000
x:@0.417527:0.274389:0.425002:0.274389:0.425002:0.257920:0.417527:0.257920:0.000000
lo que permite definir dos rectas asíntotas dadas como::@0.108242:0.303697:0.501731:0.303697:0.501731:0.287200:0.108242:0.287200:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.226955:0.338514:0.236530:0.338514:0.236530:0.322046:0.226955:0.322046:0.000000
1:@0.236526:0.341674:0.241479:0.341674:0.241479:0.332055:0.236526:0.332055:0.000000
 =   ( ,  )     |   =       ,:@0.241478:0.338396:0.423307:0.338396:0.423307:0.321898:0.241478:0.321898:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.274807:0.338511:0.296866:0.338511:0.296866:0.322043:0.274807:0.322043:0.000000:0.000000:0.000000
:@0.306960:0.337877:0.321613:0.337877:0.321613:0.324504:0.306960:0.324504:0.000000
:@0.325755:0.337309:0.339059:0.337309:0.339059:0.324447:0.325755:0.324447:0.000000
2:@0.339058:0.332044:0.344011:0.332044:0.344011:0.322426:0.339058:0.322426:0.000000
y:@0.357304:0.338511:0.364991:0.338511:0.364991:0.322043:0.357304:0.322043:0.000000
x  :@0.404793:0.338511:0.420552:0.338511:0.420552:0.322043:0.404793:0.322043:0.000000:0.000000:0.000000
R:@0.226956:0.373213:0.236530:0.373213:0.236530:0.356744:0.226956:0.356744:0.000000
2:@0.236526:0.376375:0.241479:0.376375:0.241479:0.366757:0.236526:0.366757:0.000000
 =   ( ,  )     |   = –      .:@0.241478:0.373097:0.433807:0.373097:0.433807:0.356599:0.241478:0.356599:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.274807:0.373213:0.296866:0.373213:0.296866:0.356744:0.274807:0.356744:0.000000:0.000000:0.000000
:@0.306960:0.372579:0.321613:0.372579:0.321613:0.359205:0.306960:0.359205:0.000000
:@0.325755:0.372010:0.339059:0.372010:0.339059:0.359148:0.325755:0.359148:0.000000
2:@0.339058:0.366745:0.344011:0.366745:0.344011:0.357127:0.339058:0.357127:0.000000
y:@0.357304:0.373213:0.364991:0.373213:0.364991:0.356744:0.357304:0.356744:0.000000
x  :@0.415293:0.373213:0.431052:0.373213:0.431052:0.356744:0.415293:0.356744:0.000000:0.000000:0.000000
En la Figura 2.38., se muestran con línea punteada estas dos rectas.:@0.108224:0.407799:0.576634:0.407799:0.576634:0.391301:0.108224:0.391301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejercicios resueltos:@0.108224:0.442876:0.238879:0.442876:0.238879:0.426089:0.108224:0.426089:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1.:@0.108224:0.460068:0.120496:0.460068:0.120496:0.443353:0.108224:0.443353:0.000000:0.000000
  La ecuación cartesiana de una hipérbola es ( ,  )    , tal que :@0.120496:0.459851:0.575057:0.459851:0.575057:0.443353:0.120496:0.443353:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.445652:0.459967:0.467711:0.459967:0.467711:0.443498:0.445652:0.443498:0.000000:0.000000:0.000000
:@0.477821:0.459332:0.492474:0.459332:0.492474:0.445959:0.477821:0.445959:0.000000
:@0.496616:0.458764:0.509920:0.458764:0.509920:0.445902:0.496616:0.445902:0.000000
2:@0.509919:0.453499:0.514872:0.453499:0.514872:0.443881:0.509919:0.443881:0.000000
x:@0.131975:0.477317:0.139450:0.477317:0.139450:0.460849:0.131975:0.460849:0.000000
2:@0.139451:0.470850:0.144404:0.470850:0.144404:0.461232:0.139451:0.461232:0.000000
 –   = 1. Entonces, la hipérbola es equilátera, sus focos son:@0.144405:0.477202:0.560200:0.477202:0.560200:0.460704:0.144405:0.460704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.163188:0.477317:0.170875:0.477317:0.170875:0.460849:0.163188:0.460849:0.000000
2:@0.170874:0.470850:0.175827:0.470850:0.175827:0.461232:0.170874:0.461232:0.000000
 :@0.108226:0.494552:0.112368:0.494552:0.112368:0.478055:0.108226:0.478055:0.000000
F:@0.131961:0.494668:0.139513:0.494668:0.139513:0.478199:0.131961:0.478199:0.000000
:@0.134119:0.492528:0.140534:0.492528:0.140534:0.476710:0.134119:0.476710:0.000000
1:@0.139009:0.497830:0.143962:0.497830:0.143962:0.488212:0.139009:0.488212:0.000000
 = (–   2 , 0),    = (   2 , 0), pues   = 1 y   =    2  .  En la Figura :@0.143961:0.494552:0.571381:0.494552:0.571381:0.478055:0.143961:0.478055:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F:@0.236954:0.494668:0.244506:0.494668:0.244506:0.478199:0.236954:0.478199:0.000000
:@0.239112:0.492528:0.245527:0.492528:0.245527:0.476710:0.239112:0.476710:0.000000
2:@0.243984:0.497830:0.248938:0.497830:0.248938:0.488212:0.243984:0.488212:0.000000
a:@0.364183:0.494668:0.373160:0.494668:0.373160:0.478199:0.364183:0.478199:0.000000
c:@0.416854:0.494668:0.424040:0.494668:0.424040:0.478199:0.416854:0.478199:0.000000
a:@0.466269:0.494668:0.475247:0.494668:0.475247:0.478199:0.466269:0.478199:0.000000
2.38., se muestra el conjunto  (0, 1, 1) = {( ,  )     |   –   = 1}.:@0.131979:0.511903:0.590804:0.511903:0.590804:0.495406:0.131979:0.495406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℋ:@0.334278:0.518977:0.350690:0.518977:0.350690:0.500842:0.334278:0.500842:0.000000
:@0.357732:0.509879:0.364147:0.509879:0.364147:0.494061:0.357732:0.494061:0.000000
x y:@0.430535:0.512019:0.452305:0.512019:0.452305:0.495550:0.430535:0.495550:0.000000:0.000000:0.000000
:@0.462107:0.511385:0.476760:0.511385:0.476760:0.498011:0.462107:0.498011:0.000000
:@0.480718:0.510816:0.494022:0.510816:0.494022:0.497954:0.480718:0.497954:0.000000
2:@0.493929:0.505551:0.498882:0.505551:0.498882:0.495933:0.493929:0.495933:0.000000
x:@0.511831:0.512019:0.519306:0.512019:0.519306:0.495550:0.511831:0.495550:0.000000
2:@0.519208:0.505551:0.524161:0.505551:0.524161:0.495933:0.519208:0.495933:0.000000
y:@0.542599:0.512019:0.550286:0.512019:0.550286:0.495550:0.542599:0.495550:0.000000
2:@0.550190:0.505551:0.555143:0.505551:0.555143:0.495933:0.550190:0.495933:0.000000
 :@0.108229:0.546605:0.112371:0.546605:0.112371:0.530107:0.108229:0.530107:0.000000
De la ecuación ( ,  )    , tal que   –   = 1, se obtiene:@0.131964:0.546605:0.527918:0.546605:0.527918:0.530107:0.131964:0.530107:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.246880:0.546720:0.268938:0.546720:0.268938:0.530252:0.246880:0.530252:0.000000:0.000000:0.000000
:@0.279044:0.546086:0.293696:0.546086:0.293696:0.532713:0.279044:0.532713:0.000000
:@0.297838:0.545518:0.311143:0.545518:0.311143:0.532656:0.297838:0.532656:0.000000
2:@0.311143:0.540253:0.316096:0.540253:0.316096:0.530635:0.311143:0.530635:0.000000
x:@0.376281:0.546720:0.383756:0.546720:0.383756:0.530252:0.376281:0.530252:0.000000
2:@0.383755:0.540253:0.388708:0.540253:0.388708:0.530635:0.383755:0.530635:0.000000
y:@0.407492:0.546720:0.415179:0.546720:0.415179:0.530252:0.407492:0.530252:0.000000
2:@0.415177:0.540253:0.420130:0.540253:0.420130:0.530635:0.415177:0.530635:0.000000
 :@0.108226:0.563955:0.112368:0.563955:0.112368:0.547458:0.108226:0.547458:0.000000
y:@0.131961:0.564071:0.139648:0.564071:0.139648:0.547602:0.131961:0.547602:0.000000
2:@0.139567:0.557604:0.144520:0.557604:0.144520:0.547986:0.139567:0.547986:0.000000
 –   = 1, y como   ≥ 0, se sigue que   – 1 ≥ 0, con lo que | | ≥ 1,:@0.144463:0.563955:0.595783:0.563955:0.595783:0.547458:0.144463:0.547458:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.162573:0.564071:0.170048:0.564071:0.170048:0.547602:0.162573:0.547602:0.000000
2:@0.169937:0.557604:0.174890:0.557604:0.174890:0.547986:0.169937:0.547986:0.000000
y:@0.264995:0.564071:0.272682:0.564071:0.272682:0.547602:0.264995:0.547602:0.000000
2:@0.272549:0.557604:0.277502:0.557604:0.277502:0.547986:0.272549:0.547986:0.000000
x:@0.398798:0.564071:0.406272:0.564071:0.406272:0.547602:0.398798:0.547602:0.000000
2:@0.406133:0.557604:0.411086:0.557604:0.411086:0.547986:0.406133:0.547986:0.000000
x:@0.553975:0.564071:0.561450:0.564071:0.561450:0.547602:0.553975:0.547602:0.000000
 :@0.108237:0.581306:0.112379:0.581306:0.112379:0.564809:0.108237:0.564809:0.000000
es decir, :@0.131971:0.581306:0.192281:0.581306:0.192281:0.564809:0.131971:0.564809:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.192869:0.581422:0.204486:0.581422:0.204486:0.564953:0.192869:0.564953:0.000000:0.000000
:@0.205079:0.580788:0.219731:0.580788:0.219731:0.567414:0.205079:0.567414:0.000000
 ]–∞, –1]   [1, ∞[. Para :@0.219732:0.581306:0.393555:0.581306:0.393555:0.564809:0.219732:0.564809:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
<:@0.291198:0.580788:0.305850:0.580788:0.305850:0.567414:0.291198:0.567414:0.000000
x :@0.394152:0.581422:0.405769:0.581422:0.405769:0.564953:0.394152:0.564953:0.000000:0.000000
:@0.406349:0.580788:0.421001:0.580788:0.421001:0.567414:0.406349:0.567414:0.000000
 ]–∞, –1] de la ecuación :@0.421000:0.581306:0.599915:0.581306:0.599915:0.564809:0.421000:0.564809:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.131983:0.598773:0.139670:0.598773:0.139670:0.582304:0.131983:0.582304:0.000000
2:@0.139662:0.592305:0.144615:0.592305:0.144615:0.582687:0.139662:0.582687:0.000000
 –   = 1, se obtiene la rama de hipérbola que se muestra a la :@0.144616:0.598657:0.599911:0.598657:0.599911:0.582159:0.144616:0.582159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.166289:0.598773:0.173764:0.598773:0.173764:0.582304:0.166289:0.582304:0.000000
2:@0.173765:0.592305:0.178718:0.592305:0.178718:0.582687:0.173765:0.582687:0.000000
izquierda y para :@0.131980:0.616008:0.247841:0.616008:0.247841:0.599510:0.131980:0.599510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x :@0.247860:0.616123:0.259477:0.616123:0.259477:0.599655:0.247860:0.599655:0.000000:0.000000
:@0.259502:0.615489:0.274155:0.615489:0.274155:0.602116:0.259502:0.602116:0.000000
 [1, ∞[, y de la ecuación   –   = 1, se obtiene :@0.274155:0.616008:0.599899:0.616008:0.599899:0.599510:0.274155:0.599510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.443977:0.616123:0.451664:0.616123:0.451664:0.599655:0.443977:0.599655:0.000000
2:@0.451682:0.609656:0.456635:0.609656:0.456635:0.600038:0.451682:0.600038:0.000000
x:@0.475458:0.616123:0.482933:0.616123:0.482933:0.599655:0.475458:0.599655:0.000000
2:@0.482939:0.609656:0.487892:0.609656:0.487892:0.600038:0.482939:0.600038:0.000000
la rama de la hipérbola que se muestra a la derecha.:@0.131985:0.633358:0.497984:0.633358:0.497984:0.616861:0.131985:0.616861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.:@0.108250:0.668277:0.120522:0.668277:0.120522:0.651562:0.108250:0.651562:0.000000:0.000000
  Una hipérbola tiene como ecuación canónica la siguiente:  :@0.120523:0.668060:0.550711:0.668060:0.550711:0.651562:0.120523:0.651562:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ,  )    , tal que 4  – 5  = –20.:@0.131985:0.685411:0.377499:0.685411:0.377499:0.668913:0.131985:0.668913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.137938:0.685526:0.159996:0.685526:0.159996:0.669058:0.137938:0.669058:0.000000:0.000000:0.000000
:@0.170081:0.684892:0.184734:0.684892:0.184734:0.671519:0.170081:0.671519:0.000000
:@0.188876:0.684324:0.202180:0.684324:0.202180:0.671462:0.188876:0.671462:0.000000
2:@0.202180:0.679059:0.207134:0.679059:0.207134:0.669441:0.202180:0.669441:0.000000
x:@0.275815:0.685526:0.283290:0.685526:0.283290:0.669058:0.275815:0.669058:0.000000
2:@0.283287:0.679059:0.288240:0.679059:0.288240:0.669441:0.283287:0.669441:0.000000
y:@0.315521:0.685526:0.323207:0.685526:0.323207:0.669058:0.315521:0.669058:0.000000
2:@0.323207:0.679059:0.328160:0.679059:0.328160:0.669441:0.323207:0.669441:0.000000
 :@0.108227:0.715587:0.112369:0.715587:0.112369:0.699090:0.108227:0.699090:0.000000
Dividiendo miembro a miembro para 20, la ecuación de:@0.131963:0.715587:0.528265:0.715587:0.528265:0.699090:0.131963:0.699090:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108227:0.740066:0.112369:0.740066:0.112369:0.723568:0.108227:0.723568:0.000000
la hipérbola se expresa como            –         = –1.:@0.131963:0.740066:0.472472:0.740066:0.472472:0.723568:0.131963:0.723568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108227:0.775230:0.112369:0.775230:0.112369:0.758732:0.108227:0.758732:0.000000
Se tiene   = 2,   =    5 . De la relación   =   –   resulta :@0.131963:0.775230:0.529361:0.775236:0.529361:0.758738:0.131963:0.758732:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.192147:0.775345:0.201125:0.775345:0.201125:0.758877:0.192147:0.758877:0.000000
b:@0.235610:0.775345:0.244876:0.775345:0.244876:0.758877:0.235610:0.758877:0.000000
b:@0.395685:0.775345:0.404952:0.775345:0.404952:0.758877:0.395685:0.758877:0.000000
2:@0.404960:0.768883:0.409913:0.768883:0.409913:0.759265:0.404960:0.759265:0.000000
c:@0.429005:0.775352:0.436191:0.775352:0.436191:0.758883:0.429005:0.758883:0.000000
2:@0.436190:0.768883:0.441143:0.768883:0.441143:0.759265:0.436190:0.759265:0.000000
a:@0.459927:0.775352:0.468905:0.775352:0.468905:0.758883:0.459927:0.758883:0.000000
2:@0.468904:0.768883:0.473857:0.768883:0.473857:0.759265:0.468904:0.759265:0.000000
c:@0.131976:0.792702:0.139162:0.792702:0.139162:0.776234:0.131976:0.776234:0.000000
2:@0.139161:0.786234:0.144115:0.786234:0.144115:0.776616:0.139161:0.776616:0.000000
 =   +  , con lo que   = 3.:@0.144115:0.792587:0.334707:0.792587:0.334707:0.776089:0.144115:0.776089:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.163207:0.792702:0.172184:0.792702:0.172184:0.776234:0.163207:0.776234:0.000000
2:@0.172184:0.786234:0.177137:0.786234:0.177137:0.776616:0.172184:0.776616:0.000000
b:@0.196229:0.792702:0.205496:0.792702:0.205496:0.776234:0.196229:0.776234:0.000000
2:@0.205494:0.786234:0.210447:0.786234:0.210447:0.776616:0.205494:0.776616:0.000000
c:@0.297178:0.792702:0.304364:0.792702:0.304364:0.776234:0.297178:0.776234:0.000000
 :@0.108226:0.817065:0.112368:0.817065:0.112368:0.800568:0.108226:0.800568:0.000000
Los focos de la hipérbola son   = (0, –3),    = (0, 3). El eje princi-:@0.131961:0.817065:0.589562:0.817065:0.589562:0.800568:0.131961:0.800568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F:@0.341794:0.817181:0.349346:0.817181:0.349346:0.800712:0.341794:0.800712:0.000000
:@0.343956:0.815041:0.350371:0.815041:0.350371:0.799223:0.343956:0.799223:0.000000
1:@0.348841:0.820343:0.353794:0.820343:0.353794:0.810725:0.348841:0.810725:0.000000
F:@0.430218:0.817181:0.437770:0.817181:0.437770:0.800712:0.430218:0.800712:0.000000
:@0.432376:0.815041:0.438791:0.815041:0.438791:0.799223:0.432376:0.799223:0.000000
2:@0.437248:0.820343:0.442202:0.820343:0.442202:0.810725:0.437248:0.810725:0.000000
pal coincide con el eje  . Además, los vértices de la hipérbola son :@0.131974:0.834416:0.597590:0.834416:0.597590:0.817918:0.131974:0.817918:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Y:@0.293068:0.834532:0.303201:0.834532:0.303201:0.818063:0.293068:0.818063:0.000000
v:@0.131974:0.851882:0.139757:0.851882:0.139757:0.835414:0.131974:0.835414:0.000000
:@0.133977:0.852258:0.140393:0.852258:0.140393:0.836440:0.133977:0.836440:0.000000
1:@0.140394:0.855045:0.145347:0.855045:0.145347:0.845427:0.140394:0.845427:0.000000
 = (0, –2),   = (0, –2). En la Figura 2.39. se muestra la hipérbola::@0.145348:0.851767:0.591531:0.851767:0.591531:0.835269:0.145348:0.835269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
v:@0.217631:0.851882:0.225414:0.851882:0.225414:0.835414:0.217631:0.835414:0.000000
:@0.219635:0.852258:0.226050:0.852258:0.226050:0.836440:0.219635:0.836440:0.000000
1:@0.226048:0.855045:0.231001:0.855045:0.231001:0.845427:0.226048:0.845427:0.000000
ℋ:@0.183296:0.892034:0.199707:0.892034:0.199707:0.873898:0.183296:0.873898:0.000000
(0, 2,   5 ) =   ( ,  )     |            –         = –1   .:@0.199708:0.884959:0.520708:0.884959:0.520708:0.868462:0.199708:0.868462:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.206932:0.882935:0.213348:0.882935:0.213348:0.867117:0.206932:0.867117:0.000000
x y:@0.295745:0.885075:0.317804:0.885075:0.317804:0.868606:0.295745:0.868606:0.000000:0.000000:0.000000
:@0.327896:0.884441:0.342548:0.884441:0.342548:0.871068:0.327896:0.871068:0.000000
:@0.346690:0.883873:0.359995:0.883873:0.359995:0.871010:0.346690:0.871010:0.000000
2:@0.359995:0.878608:0.364948:0.878608:0.364948:0.868990:0.359995:0.868990:0.000000
b:@0.394047:0.238860:0.403314:0.238860:0.403314:0.222391:0.394047:0.222391:0.000000
a:@0.394201:0.255199:0.403179:0.255199:0.403179:0.238730:0.394201:0.238730:0.000000
b:@0.389191:0.331000:0.398457:0.331000:0.398457:0.314531:0.389191:0.314531:0.000000
a:@0.389345:0.347339:0.398323:0.347339:0.398323:0.330870:0.389345:0.330870:0.000000
b:@0.398775:0.365957:0.408041:0.365957:0.408041:0.349488:0.398775:0.349488:0.000000
a:@0.398929:0.382296:0.407907:0.382296:0.407907:0.365827:0.398929:0.365827:0.000000
b:@0.405669:0.267195:0.414935:0.267195:0.414935:0.250726:0.405669:0.250726:0.000000
a:@0.405823:0.283533:0.414800:0.283533:0.414800:0.267065:0.405823:0.267065:0.000000
x:@0.254461:0.141959:0.261936:0.141959:0.261936:0.125490:0.254461:0.125490:0.000000
b:@0.253575:0.158297:0.262842:0.158297:0.262842:0.141829:0.253575:0.141829:0.000000
y:@0.302938:0.141959:0.310625:0.141959:0.310625:0.125490:0.302938:0.125490:0.000000
a:@0.302283:0.158297:0.311260:0.158297:0.311260:0.141829:0.302283:0.141829:0.000000
2:@0.270569:0.135974:0.275522:0.135974:0.275522:0.126356:0.270569:0.126356:0.000000
2:@0.319146:0.135974:0.324099:0.135974:0.324099:0.126356:0.319146:0.126356:0.000000
b:@0.222210:0.179981:0.231476:0.179981:0.231476:0.163512:0.222210:0.163512:0.000000
2:@0.231477:0.173512:0.236430:0.173512:0.236430:0.163894:0.231477:0.163894:0.000000
a:@0.222355:0.196326:0.231333:0.196326:0.231333:0.179857:0.222355:0.179857:0.000000
2:@0.231333:0.189857:0.236286:0.189857:0.236286:0.180239:0.231333:0.180239:0.000000
a:@0.294339:0.179981:0.303316:0.179981:0.303316:0.163512:0.294339:0.163512:0.000000
2:@0.303316:0.173512:0.308270:0.173512:0.308270:0.163894:0.303316:0.163894:0.000000
x:@0.295091:0.196326:0.302566:0.196326:0.302566:0.179857:0.295091:0.179857:0.000000
2:@0.302564:0.189857:0.307517:0.189857:0.307517:0.180239:0.302564:0.180239:0.000000
x:@0.359269:0.733133:0.366744:0.733133:0.366744:0.716664:0.359269:0.716664:0.000000
  5:@0.354626:0.750614:0.371407:0.750614:0.371407:0.734116:0.354626:0.734116:0.000000:0.000000:0.000000
y:@0.412348:0.733133:0.420035:0.733133:0.420035:0.716664:0.412348:0.716664:0.000000
2:@0.411943:0.749356:0.420439:0.749356:0.420439:0.732858:0.411943:0.732858:0.000000
2:@0.383331:0.728395:0.388284:0.728395:0.388284:0.718777:0.383331:0.718777:0.000000
2:@0.428561:0.728395:0.433514:0.728395:0.433514:0.718777:0.428561:0.718777:0.000000
x:@0.393355:0.877609:0.400830:0.877609:0.400830:0.861141:0.393355:0.861141:0.000000
  5:@0.388713:0.895090:0.405493:0.895090:0.405493:0.878593:0.388713:0.878593:0.000000:0.000000:0.000000
y:@0.448111:0.877609:0.455798:0.877609:0.455798:0.861141:0.448111:0.861141:0.000000
2:@0.447706:0.893832:0.456202:0.893832:0.456202:0.877335:0.447706:0.877335:0.000000
2:@0.417417:0.872872:0.422370:0.872872:0.422370:0.863254:0.417417:0.863254:0.000000
2:@0.464320:0.872872:0.469274:0.872872:0.469274:0.863254:0.464320:0.863254:0.000000
p:@0.629077:0.611855:0.640557:0.611855:0.640557:0.601831:0.629077:0.601831:0.000000
 :@0.640557:0.612563:0.643439:0.612563:0.643439:0.601087:0.640557:0.601087:0.000000
Figura 2.38.:@0.643439:0.612563:0.697917:0.612563:0.697917:0.601087:0.643439:0.601087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.633749:0.523798:0.639096:0.523798:0.639096:0.512341:0.633749:0.512341:0.000000
2:@0.639096:0.519301:0.642542:0.519301:0.642542:0.512610:0.639096:0.512610:0.000000
 = :@0.642541:0.523720:0.655822:0.523720:0.655822:0.512243:0.642541:0.512243:0.000000:0.000000:0.000000
x –:@0.655822:0.523800:0.671450:0.523800:0.671450:0.512344:0.655822:0.512344:0.000000:0.000000:0.000000
2:@0.661022:0.519301:0.664468:0.519301:0.664468:0.512610:0.661022:0.512610:0.000000
1:@0.671450:0.523720:0.677361:0.523720:0.677361:0.512243:0.671450:0.512243:0.000000
y:@0.801623:0.523800:0.806971:0.523800:0.806971:0.512344:0.801623:0.512344:0.000000
2:@0.806976:0.519301:0.810421:0.519301:0.810421:0.512610:0.806976:0.512610:0.000000
 = :@0.810421:0.523720:0.823703:0.523720:0.823703:0.512243:0.810421:0.512243:0.000000:0.000000:0.000000
x –:@0.823703:0.523800:0.839331:0.523800:0.839331:0.512344:0.823703:0.512344:0.000000:0.000000:0.000000
2:@0.828903:0.519301:0.832348:0.519301:0.832348:0.512610:0.828903:0.512610:0.000000
1:@0.839331:0.523720:0.845241:0.523720:0.845241:0.512243:0.839331:0.512243:0.000000
0:@0.733907:0.551013:0.738339:0.551013:0.738339:0.542406:0.733907:0.542406:0.000000
y:@0.724473:0.496935:0.730935:0.496935:0.730935:0.483307:0.724473:0.483307:0.000000
x:@0.842991:0.557075:0.849595:0.557075:0.849595:0.543446:0.842991:0.543446:0.000000
–1:@0.726727:0.567434:0.736637:0.567434:0.736637:0.558826:0.726727:0.558826:0.000000:0.000000
1:@0.732205:0.524125:0.736637:0.524125:0.736637:0.515517:0.732205:0.515517:0.000000
1:@0.765274:0.550679:0.769706:0.550679:0.769706:0.542071:0.765274:0.542071:0.000000
2:@0.801841:0.550679:0.806274:0.550679:0.806274:0.542071:0.801841:0.542071:0.000000
–1:@0.695808:0.550679:0.705719:0.550679:0.705719:0.542071:0.695808:0.542071:0.000000:0.000000
–2:@0.667333:0.550679:0.677243:0.550679:0.677243:0.542071:0.667333:0.542071:0.000000:0.000000
F:@0.685693:0.554766:0.690618:0.554766:0.690618:0.544025:0.685693:0.544025:0.000000
:@0.687100:0.553757:0.691284:0.553757:0.691284:0.543441:0.687100:0.543441:0.000000
1:@0.689965:0.555571:0.693195:0.555571:0.693195:0.549298:0.689965:0.549298:0.000000
F:@0.786208:0.554766:0.791133:0.554766:0.791133:0.544025:0.786208:0.544025:0.000000
:@0.787615:0.553757:0.791799:0.553757:0.791799:0.543441:0.787615:0.543441:0.000000
2:@0.790479:0.555571:0.793710:0.555571:0.793710:0.549298:0.790479:0.549298:0.000000
x:@0.639706:0.533235:0.644906:0.533235:0.644906:0.521779:0.639706:0.521779:0.000000
 ≤ –1:@0.644906:0.533155:0.671402:0.533155:0.671402:0.521678:0.644906:0.521678:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.811237:0.533235:0.816437:0.533235:0.816437:0.521779:0.811237:0.521779:0.000000
 ≥ 1:@0.816437:0.533155:0.835629:0.533155:0.835629:0.521678:0.816437:0.521678:0.000000:0.000000:0.000000:0.000000
p:@0.629077:0.838796:0.640557:0.838796:0.640557:0.828771:0.629077:0.828771:0.000000
 :@0.640557:0.839504:0.643439:0.839504:0.643439:0.828027:0.640557:0.828027:0.000000
Figura 2.39.:@0.643439:0.839504:0.697917:0.839504:0.697917:0.828027:0.643439:0.828027:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.728001:0.722995:0.734463:0.722995:0.734463:0.709367:0.728001:0.709367:0.000000
x:@0.838132:0.786909:0.844736:0.786909:0.844736:0.773281:0.838132:0.773281:0.000000
0 1:@0.742460:0.780847:0.758035:0.780113:0.758035:0.771505:0.742460:0.772239:0.000000:0.000000:0.000000
1:@0.733158:0.768284:0.737590:0.768284:0.737590:0.759676:0.733158:0.759676:0.000000
–1:@0.728182:0.782730:0.737590:0.782730:0.737590:0.774123:0.728182:0.774123:0.000000:0.000000
–2:@0.728182:0.790568:0.737590:0.790568:0.737590:0.781961:0.728182:0.781961:0.000000:0.000000
–3:@0.728182:0.798406:0.737590:0.798406:0.737590:0.789799:0.728182:0.789799:0.000000:0.000000
–4:@0.728182:0.806244:0.737590:0.806244:0.737590:0.797637:0.728182:0.797637:0.000000:0.000000
2:@0.733158:0.760438:0.737590:0.760438:0.737590:0.751831:0.733158:0.751831:0.000000
3:@0.733158:0.752600:0.737590:0.752600:0.737590:0.743993:0.733158:0.743993:0.000000
4:@0.733158:0.744762:0.737590:0.744762:0.737590:0.736155:0.733158:0.736155:0.000000
–1:@0.721277:0.780120:0.731188:0.780120:0.731188:0.771513:0.721277:0.771513:0.000000:0.000000
–2:@0.706079:0.780120:0.715990:0.780120:0.715990:0.771513:0.706079:0.771513:0.000000:0.000000
–3:@0.690881:0.780120:0.700792:0.780120:0.700792:0.771513:0.690881:0.771513:0.000000:0.000000
–4:@0.675684:0.780120:0.685594:0.780120:0.685594:0.771513:0.675684:0.771513:0.000000:0.000000
2:@0.768911:0.780120:0.773343:0.780120:0.773343:0.771513:0.768911:0.771513:0.000000
3:@0.784229:0.780120:0.788662:0.780120:0.788662:0.771513:0.784229:0.771513:0.000000
4:@0.799548:0.780120:0.803980:0.780120:0.803980:0.771513:0.799548:0.771513:0.000000
F:@0.723297:0.747492:0.728223:0.747492:0.728223:0.736752:0.723297:0.736752:0.000000
:@0.724705:0.746483:0.728888:0.746483:0.728888:0.736167:0.724705:0.736167:0.000000
2:@0.727569:0.748297:0.730800:0.748297:0.730800:0.742024:0.727569:0.742024:0.000000
F:@0.719947:0.801556:0.724872:0.801556:0.724872:0.790816:0.719947:0.790816:0.000000
:@0.721354:0.800547:0.725538:0.800547:0.725538:0.790231:0.721354:0.790231:0.000000
1:@0.724219:0.802360:0.727449:0.802360:0.727449:0.796088:0.724219:0.796088:0.000000
y:@0.745479:0.818391:0.750827:0.818391:0.750827:0.806935:0.745479:0.806935:0.000000
 = –        :@0.750827:0.818311:0.794463:0.818311:0.794463:0.806834:0.750827:0.806834:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x +5:@0.794463:0.818391:0.816295:0.818391:0.816295:0.806935:0.794463:0.806935:0.000000:0.000000:0.000000:0.000000
2:@0.799661:0.813892:0.803107:0.813892:0.803107:0.807201:0.799661:0.807201:0.000000
2:@0.776014:0.813120:0.781986:0.813120:0.781986:0.801522:0.776014:0.801522:0.000000
 5:@0.774483:0.825694:0.783436:0.825694:0.783436:0.814096:0.774483:0.814096:0.000000:0.000000
y:@0.655182:0.725884:0.660529:0.725884:0.660529:0.714427:0.655182:0.714427:0.000000
 =        :@0.660529:0.725803:0.693981:0.725803:0.693981:0.714327:0.660529:0.714327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x +5:@0.693981:0.725884:0.715812:0.725884:0.715812:0.714427:0.693981:0.714427:0.000000:0.000000:0.000000:0.000000
2:@0.699179:0.721384:0.702625:0.721384:0.702625:0.714694:0.699179:0.714694:0.000000
2:@0.676910:0.720399:0.682883:0.720399:0.682883:0.708801:0.676910:0.708801:0.000000
 5:@0.675379:0.732973:0.684332:0.732973:0.684332:0.721375:0.675379:0.721375:0.000000:0.000000
5:@0.780425:0.770899:0.786335:0.770899:0.786335:0.759422:0.780425:0.759422:0.000000
–   5:@0.686933:0.770899:0.705937:0.770899:0.705937:0.759422:0.686933:0.759422:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.685849:0.104916:0.783472:0.104916:0.783472:0.089444:0.685849:0.089444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comunicacional:@0.685849:0.117484:0.797808:0.117484:0.797808:0.102012:0.685849:0.102012:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Aprende la definición de :@0.679277:0.141957:0.843425:0.141957:0.843425:0.126894:0.679277:0.126894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hipérbola equilátera::@0.639541:0.157799:0.772010:0.157799:0.772010:0.142736:0.639541:0.142736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En el caso particular en que   =   :@0.639541:0.180770:0.850428:0.180770:0.850428:0.165707:0.639541:0.165707:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.813610:0.180876:0.846646:0.180876:0.846646:0.165839:0.813610:0.165839:0.000000:0.000000:0.000000
de la relación   =   –  , o bien,   :@0.639541:0.196612:0.849086:0.196612:0.849086:0.181549:0.639541:0.181549:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.724907:0.196718:0.733368:0.196718:0.733368:0.181681:0.724907:0.181681:0.000000
2:@0.733109:0.190812:0.737632:0.190812:0.737632:0.182030:0.733109:0.182030:0.000000
c:@0.754118:0.196718:0.760679:0.196718:0.760679:0.181681:0.754118:0.181681:0.000000
2:@0.760414:0.190812:0.764936:0.190812:0.764936:0.182030:0.760414:0.182030:0.000000
a:@0.781142:0.196718:0.789339:0.196718:0.789339:0.181681:0.781142:0.181681:0.000000
2:@0.789074:0.190812:0.793596:0.190812:0.793596:0.182030:0.789074:0.182030:0.000000
c:@0.639548:0.212560:0.646109:0.212560:0.646109:0.197523:0.639548:0.197523:0.000000
2:@0.645846:0.206654:0.650368:0.206654:0.650368:0.197872:0.645846:0.197872:0.000000
 =   +  , se obtiene   = ±   2 . :@0.650215:0.212454:0.849398:0.212454:0.849398:0.197391:0.650215:0.197391:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.666855:0.212560:0.675052:0.212560:0.675052:0.197523:0.666855:0.197523:0.000000
2:@0.674787:0.206654:0.679310:0.206654:0.679310:0.197872:0.674787:0.197872:0.000000
b:@0.695797:0.212560:0.704257:0.212560:0.704257:0.197523:0.695797:0.197523:0.000000
2:@0.703992:0.206654:0.708514:0.206654:0.708514:0.197872:0.703992:0.197872:0.000000
c:@0.781940:0.212560:0.788501:0.212560:0.788501:0.197523:0.781940:0.197523:0.000000
a:@0.832529:0.212560:0.840726:0.212560:0.840726:0.197523:0.832529:0.197523:0.000000
Los focos   y   de la hipérbola:@0.639549:0.228296:0.833885:0.228296:0.833885:0.213233:0.639549:0.213233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F:@0.700795:0.228402:0.707690:0.228402:0.707690:0.213366:0.700795:0.213366:0.000000
:@0.702765:0.226448:0.708623:0.226448:0.708623:0.212006:0.702765:0.212006:0.000000
1:@0.707217:0.230659:0.711739:0.230659:0.711739:0.221878:0.707217:0.221878:0.000000
F:@0.726443:0.228402:0.733338:0.228402:0.733338:0.213366:0.726443:0.213366:0.000000
:@0.728413:0.226448:0.734271:0.226448:0.734271:0.212006:0.728413:0.212006:0.000000
2:@0.732863:0.230659:0.737385:0.230659:0.737385:0.221878:0.732863:0.221878:0.000000
son   = (–   2  , 0),   = (   2  , 0). :@0.639550:0.251267:0.848501:0.251266:0.848501:0.236203:0.639550:0.236204:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F:@0.665739:0.251371:0.672634:0.251371:0.672634:0.236335:0.665739:0.236335:0.000000
:@0.667709:0.249418:0.673567:0.249418:0.673567:0.234976:0.667709:0.234976:0.000000
1:@0.672161:0.253629:0.676683:0.253629:0.676683:0.244848:0.672161:0.244848:0.000000
a:@0.725864:0.251372:0.734061:0.251372:0.734061:0.236335:0.725864:0.236335:0.000000
F:@0.761516:0.251371:0.768411:0.251371:0.768411:0.236335:0.761516:0.236335:0.000000
:@0.763486:0.249418:0.769343:0.249418:0.769343:0.234976:0.763486:0.234976:0.000000
2:@0.767937:0.253629:0.772460:0.253629:0.772460:0.244848:0.767937:0.244848:0.000000
a:@0.812318:0.251372:0.820515:0.251372:0.820515:0.236335:0.812318:0.236335:0.000000
A la hipérbola:@0.639549:0.274237:0.727321:0.274237:0.727321:0.259174:0.639549:0.259174:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℋ:@0.639549:0.305626:0.654532:0.305626:0.654532:0.289069:0.639549:0.289069:0.000000
(0,  ,  ) =  ( ,  )     |:@0.654534:0.299168:0.799853:0.299168:0.799853:0.284105:0.654534:0.284105:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.661130:0.297319:0.666987:0.297319:0.666987:0.282878:0.661130:0.282878:0.000000
a b:@0.673196:0.299273:0.696150:0.299273:0.696150:0.284237:0.673196:0.284237:0.000000:0.000000:0.000000
x y:@0.728315:0.299273:0.748455:0.299273:0.748455:0.284237:0.728315:0.284237:0.000000:0.000000:0.000000
:@0.757670:0.298694:0.771048:0.298694:0.771048:0.286484:0.757670:0.286484:0.000000
:@0.774829:0.298175:0.786977:0.298175:0.786977:0.286432:0.774829:0.286432:0.000000
2:@0.786975:0.293368:0.791497:0.293368:0.791497:0.284587:0.786975:0.284587:0.000000
x:@0.646256:0.326466:0.653081:0.326466:0.653081:0.311430:0.646256:0.311430:0.000000
a:@0.645570:0.341383:0.653767:0.341383:0.653767:0.326347:0.645570:0.326347:0.000000
2:@0.661734:0.321044:0.666256:0.321044:0.666256:0.312263:0.661734:0.312263:0.000000
 – :@0.668870:0.331570:0.688131:0.331570:0.688131:0.316507:0.668870:0.316507:0.000000:0.000000:0.000000
y:@0.694741:0.326466:0.701759:0.326466:0.701759:0.311430:0.694741:0.311430:0.000000
b:@0.694020:0.341383:0.702480:0.341383:0.702480:0.326347:0.694020:0.326347:0.000000
2:@0.709966:0.321044:0.714488:0.321044:0.714488:0.312263:0.709966:0.312263:0.000000
 = 1 se la denomina:@0.714991:0.331570:0.846087:0.331570:0.846087:0.316507:0.714991:0.316507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.744045:0.331636:0.747901:0.331636:0.747901:0.316277:0.744045:0.316277:0.000000
hipérbola equilátera. Las asíntotas :@0.639545:0.361670:0.851466:0.361670:0.851466:0.346606:0.639545:0.346606:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de esta hipérbola están definidas :@0.639545:0.377512:0.851466:0.377512:0.851466:0.362448:0.639545:0.362448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como::@0.639545:0.393354:0.679158:0.393354:0.679158:0.378290:0.639545:0.378290:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.639545:0.416747:0.648288:0.416747:0.648288:0.401710:0.639545:0.401710:0.000000
1:@0.648027:0.419625:0.652550:0.419625:0.652550:0.410844:0.648027:0.410844:0.000000
 = {( ,  )     |:@0.652396:0.416634:0.749247:0.416634:0.749247:0.401571:0.652396:0.401571:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.679291:0.416739:0.698640:0.416739:0.698640:0.401703:0.679291:0.401703:0.000000:0.000000:0.000000
:@0.707064:0.416160:0.720442:0.416160:0.720442:0.403950:0.707064:0.403950:0.000000
:@0.724224:0.415641:0.736371:0.415641:0.736371:0.403898:0.724224:0.403898:0.000000
2:@0.736371:0.410833:0.740893:0.410833:0.740893:0.402052:0.736371:0.402052:0.000000
   = :@0.749247:0.416700:0.778034:0.416700:0.778034:0.401341:0.749247:0.401341:0.000000:0.000000:0.000000:0.000000:0.000000
y x:@0.753103:0.416808:0.784993:0.416808:0.784993:0.401475:0.753103:0.401475:0.000000:0.000000:0.000000
},:@0.784993:0.416634:0.792592:0.416634:0.792592:0.401571:0.784993:0.401571:0.000000:0.000000
R:@0.639541:0.440027:0.648283:0.440027:0.648283:0.424990:0.639541:0.424990:0.000000
2:@0.648027:0.442907:0.652550:0.442907:0.652550:0.434125:0.648027:0.434125:0.000000
 = {( ,  )     |:@0.652396:0.439915:0.749247:0.439915:0.749247:0.424853:0.652396:0.424852:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.679291:0.440021:0.698640:0.440021:0.698640:0.424984:0.679291:0.424984:0.000000:0.000000:0.000000
:@0.707064:0.439442:0.720442:0.439442:0.720442:0.427232:0.707064:0.427232:0.000000
:@0.724224:0.438923:0.736371:0.438923:0.736371:0.427179:0.724224:0.427179:0.000000
2:@0.736371:0.434114:0.740893:0.434114:0.740893:0.425333:0.736371:0.425333:0.000000
   = –:@0.749247:0.439981:0.787809:0.439981:0.787809:0.424622:0.749247:0.424622:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.753103:0.440089:0.760259:0.440089:0.760259:0.424757:0.753103:0.424757:0.000000
x:@0.787809:0.440089:0.794768:0.440089:0.794768:0.424757:0.787809:0.424757:0.000000
}.:@0.794768:0.439915:0.802367:0.439915:0.802367:0.424852:0.794768:0.424852:0.000000:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000