93:@0.922460:0.966765:0.939432:0.966765:0.939432:0.950778:0.922460:0.950778:0.000000:0.000000
En este caso, la pendiente de dicha recta   sí está definida, por lo que :@0.108233:0.096194:0.599954:0.096194:0.599954:0.079697:0.108233:0.079697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.398133:0.096310:0.405974:0.096310:0.405974:0.079841:0.398133:0.079841:0.000000
se puede obtener su ecuación cartesiana.:@0.108233:0.113545:0.399404:0.113545:0.399404:0.097047:0.108233:0.097047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Supongamos que la ecuación cartesiana de la recta tangente   a la :@0.108233:0.148246:0.599815:0.148246:0.599815:0.131749:0.108233:0.131749:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.556738:0.148362:0.564579:0.148362:0.564579:0.131893:0.556738:0.131893:0.000000
elipse  (0,  ,  ) en el punto   = ( ,  ) está definida como::@0.108233:0.165597:0.516481:0.165597:0.516481:0.149100:0.108233:0.149100:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E:@0.152158:0.165713:0.160114:0.165713:0.160114:0.149244:0.152158:0.149244:0.000000
:@0.167339:0.163573:0.173754:0.163573:0.173754:0.147755:0.167339:0.147755:0.000000
a b:@0.180555:0.165713:0.205696:0.165713:0.205696:0.149244:0.180555:0.149244:0.000000:0.000000:0.000000
u:@0.301733:0.165713:0.310942:0.165713:0.310942:0.149244:0.301733:0.149244:0.000000
:@0.304199:0.166089:0.310615:0.166089:0.310615:0.150271:0.304199:0.150271:0.000000
x y:@0.335659:0.165713:0.362321:0.165713:0.362321:0.149244:0.335659:0.149244:0.000000:0.000000:0.000000
0:@0.343033:0.168875:0.347986:0.168875:0.347986:0.159257:0.343033:0.159257:0.000000
0:@0.362225:0.168875:0.367178:0.168875:0.367178:0.159257:0.362225:0.159257:0.000000
( ,  )     tal que   –   =  (  –  ),:@0.222535:0.200299:0.481465:0.200299:0.481465:0.183801:0.222535:0.183801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.228488:0.200414:0.250547:0.200414:0.250547:0.183946:0.228488:0.183946:0.000000:0.000000:0.000000
:@0.260641:0.199780:0.275294:0.199780:0.275294:0.186407:0.260641:0.186407:0.000000
:@0.279436:0.199212:0.292741:0.199212:0.292741:0.186350:0.279436:0.186350:0.000000
2:@0.292741:0.193947:0.297694:0.193947:0.297694:0.184329:0.292741:0.184329:0.000000
y y:@0.355122:0.200414:0.389280:0.200414:0.389280:0.183946:0.355122:0.183946:0.000000:0.000000:0.000000
0:@0.389278:0.203577:0.394231:0.203577:0.394231:0.193959:0.389278:0.193959:0.000000
m x x:@0.413324:0.200414:0.467806:0.200414:0.467806:0.183946:0.413324:0.183946:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.467805:0.203577:0.472758:0.203577:0.472758:0.193959:0.467805:0.193959:0.000000
donde       es la pendiente de dicha recta   y de la que por el mo-:@0.108239:0.235000:0.595760:0.235000:0.595760:0.218503:0.108239:0.218503:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.158907:0.235116:0.173702:0.235116:0.173702:0.218647:0.158907:0.218647:0.000000
:@0.177861:0.234482:0.192514:0.234482:0.192514:0.221108:0.177861:0.221108:0.000000
:@0.196686:0.233913:0.209990:0.233913:0.209990:0.221051:0.196686:0.221051:0.000000
L:@0.428291:0.235116:0.436132:0.235116:0.436132:0.218647:0.428291:0.218647:0.000000
mento no se conoce. Cuando      , la ecuación precedente genera :@0.108236:0.252351:0.599934:0.252351:0.599934:0.235853:0.108236:0.235853:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.322506:0.252467:0.337301:0.252467:0.337301:0.235998:0.322506:0.235998:0.000000
:@0.341616:0.251832:0.356268:0.251832:0.356268:0.238459:0.341616:0.238459:0.000000
:@0.360625:0.251264:0.373929:0.251264:0.373929:0.238402:0.360625:0.238402:0.000000
n:@0.108227:0.269817:0.117590:0.269817:0.117590:0.253349:0.108227:0.253349:0.000000
 haz de rectas que pasan por ( ,  ). En la Figura 2.33. se muestran al-:@0.117494:0.269702:0.595712:0.269702:0.595712:0.253204:0.117494:0.253204:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.327614:0.269817:0.354231:0.269817:0.354231:0.253349:0.327614:0.253349:0.000000:0.000000:0.000000
0:@0.335057:0.272980:0.340010:0.272980:0.340010:0.263362:0.335057:0.263362:0.000000
0:@0.354141:0.272980:0.359095:0.272980:0.359095:0.263362:0.354141:0.263362:0.000000
gunas rectas de este haz (cuatro rectas  ,  ,  ,   y la recta tangente  ).:@0.108224:0.287053:0.595763:0.287053:0.595763:0.270555:0.108224:0.270555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L L L L:@0.377090:0.287168:0.440777:0.287168:0.440777:0.270699:0.377090:0.270699:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.384795:0.290330:0.389748:0.290330:0.389748:0.280712:0.384795:0.280712:0.000000
2:@0.403420:0.290330:0.408374:0.290330:0.408374:0.280712:0.403420:0.280712:0.000000
3:@0.422047:0.290330:0.427001:0.290330:0.427001:0.280712:0.422047:0.280712:0.000000
4:@0.440674:0.290330:0.445627:0.290330:0.445627:0.280712:0.440674:0.280712:0.000000
L:@0.579445:0.287168:0.587286:0.287168:0.587286:0.270699:0.579445:0.270699:0.000000
La ecuación cartesiana de la elipse  (0,  ,  ) está definida como: :@0.108236:0.321754:0.560910:0.321754:0.560910:0.305256:0.108236:0.305256:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E:@0.353867:0.321870:0.361823:0.321870:0.361823:0.305401:0.353867:0.305401:0.000000
:@0.369049:0.319730:0.375465:0.319730:0.375465:0.303912:0.369049:0.303912:0.000000
a b:@0.382265:0.321870:0.407407:0.321870:0.407407:0.305401:0.382265:0.305401:0.000000:0.000000:0.000000
( ,  )     tal que         +          = 1.:@0.229935:0.349790:0.474079:0.349797:0.474079:0.333299:0.229935:0.333292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.235888:0.349906:0.257947:0.349906:0.257947:0.333437:0.235888:0.333437:0.000000:0.000000:0.000000
:@0.268031:0.349278:0.282683:0.349278:0.282683:0.335905:0.268031:0.335905:0.000000
:@0.286825:0.348710:0.300130:0.348710:0.300130:0.335848:0.286825:0.335848:0.000000
2:@0.300130:0.343445:0.305083:0.343445:0.305083:0.333827:0.300130:0.333827:0.000000
En el punto de tangencia,   = ( ,  )    (0,  ,  ); luego,:@0.108231:0.381476:0.495880:0.381481:0.495880:0.364983:0.108231:0.364979:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.292812:0.381592:0.302021:0.381592:0.302021:0.365123:0.292812:0.365123:0.000000
:@0.295278:0.381968:0.301693:0.381968:0.301693:0.366150:0.295278:0.366150:0.000000
x y:@0.326738:0.381592:0.353749:0.381597:0.353749:0.365128:0.326738:0.365123:0.000000:0.000000:0.000000
0:@0.334211:0.384759:0.339164:0.384759:0.339164:0.375141:0.334211:0.375141:0.000000
0:@0.353748:0.384759:0.358701:0.384759:0.358701:0.375141:0.353748:0.375141:0.000000
:@0.368796:0.380962:0.383449:0.380962:0.383449:0.367589:0.368796:0.367589:0.000000
E:@0.387590:0.381597:0.395547:0.381597:0.395547:0.365128:0.387590:0.365128:0.000000
:@0.402771:0.379457:0.409187:0.379457:0.409187:0.363638:0.402771:0.363638:0.000000
a b:@0.415987:0.381597:0.441128:0.381597:0.441128:0.365128:0.415987:0.365128:0.000000:0.000000:0.000000
          +          = 1.:@0.292073:0.414679:0.411922:0.414679:0.411922:0.398181:0.292073:0.398181:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108225:0.432029:0.112367:0.432029:0.112367:0.415532:0.108225:0.415532:0.000000
Se prueba que la pendiente   =               y la ecuación de la recta es::@0.108225:0.449380:0.590062:0.449380:0.590062:0.432882:0.108225:0.432882:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.306730:0.449496:0.321526:0.449496:0.321526:0.433027:0.306730:0.433027:0.000000
( ,  )     tal que   –   =                  .:@0.108225:0.484082:0.372190:0.484077:0.372190:0.467579:0.108225:0.467584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.114178:0.484197:0.136236:0.484197:0.136236:0.467729:0.114178:0.467729:0.000000:0.000000:0.000000
:@0.146338:0.483558:0.160991:0.483558:0.160991:0.470185:0.146338:0.470185:0.000000
:@0.165133:0.482990:0.178437:0.482990:0.178437:0.470127:0.165133:0.470127:0.000000
2:@0.178437:0.477725:0.183391:0.477725:0.183391:0.468107:0.178437:0.468107:0.000000
y y:@0.240821:0.484192:0.274978:0.484192:0.274978:0.467724:0.240821:0.467724:0.000000:0.000000:0.000000
0:@0.274976:0.487355:0.279930:0.487355:0.279930:0.477736:0.274976:0.477736:0.000000
Ejercicio resuelto:@0.108236:0.522711:0.226215:0.522711:0.226215:0.505924:0.108236:0.505924:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Considérese la elipse  (0, 4, 1) y   =   –2, –           .:@0.108236:0.539686:0.450985:0.539686:0.450985:0.523188:0.108236:0.523188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E:@0.257983:0.539801:0.265940:0.539801:0.265940:0.523333:0.257983:0.523333:0.000000
:@0.273166:0.537662:0.279582:0.537662:0.279582:0.521843:0.273166:0.521843:0.000000
u:@0.332330:0.539801:0.341539:0.539801:0.341539:0.523333:0.332330:0.523333:0.000000
:@0.334796:0.540177:0.341211:0.540177:0.341211:0.524359:0.334796:0.524359:0.000000
Determinamos la ecuación cartesiana de la recta tangente   en:@0.108236:0.574387:0.553202:0.574387:0.553202:0.557890:0.108236:0.557890:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.523669:0.574503:0.531509:0.574503:0.531509:0.558034:0.523669:0.558034:0.000000
el punto  (0, 4, 1)  =   –2, –          . Primeramente, verificamos que:@0.108236:0.598866:0.565262:0.598866:0.565262:0.582369:0.108236:0.582369:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E:@0.172486:0.598982:0.180443:0.598982:0.180443:0.582513:0.172486:0.582513:0.000000
:@0.187667:0.596842:0.194082:0.596842:0.194082:0.581024:0.187667:0.581024:0.000000
u:@0.108236:0.623461:0.117445:0.623461:0.117445:0.606992:0.108236:0.606992:0.000000
:@0.110702:0.623837:0.117118:0.623837:0.117118:0.608019:0.110702:0.608019:0.000000
    (0, 4, 1). En efecto, la ecuación cartesiana de la elipse es: :@0.117118:0.623345:0.540975:0.623353:0.540975:0.606855:0.117118:0.606848:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.121256:0.622834:0.135909:0.622834:0.135909:0.609461:0.121256:0.609461:0.000000
E:@0.140050:0.623469:0.148007:0.623469:0.148007:0.607000:0.140050:0.607000:0.000000
:@0.155231:0.621329:0.161646:0.621329:0.161646:0.605510:0.155231:0.605510:0.000000
( ,  )    , tal que         +         = 1.:@0.108224:0.658054:0.350999:0.658054:0.350999:0.641557:0.108224:0.641557:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.114177:0.658170:0.136236:0.658170:0.136236:0.641701:0.114177:0.641701:0.000000:0.000000:0.000000
:@0.146338:0.657536:0.160991:0.657536:0.160991:0.644162:0.146338:0.644162:0.000000
:@0.165133:0.656967:0.178437:0.656967:0.178437:0.644105:0.165133:0.644105:0.000000
2:@0.178437:0.651701:0.183391:0.651701:0.183391:0.642083:0.178437:0.642083:0.000000
Luego, para   = –2, y = –        se tiene   –       +   –          = 1 que muestra:@0.108237:0.693219:0.595987:0.693219:0.595987:0.676721:0.108237:0.676721:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.192870:0.693334:0.200344:0.693334:0.200344:0.676865:0.192870:0.676865:0.000000
que      (0, 4, 1).:@0.108237:0.724826:0.232197:0.724831:0.232197:0.708333:0.108237:0.708328:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.139387:0.724942:0.148596:0.724942:0.148596:0.708473:0.139387:0.708473:0.000000
:@0.141855:0.725317:0.148270:0.725317:0.148270:0.709499:0.141855:0.709499:0.000000
:@0.152407:0.724312:0.167060:0.724312:0.167060:0.710939:0.152407:0.710939:0.000000
E:@0.171203:0.724947:0.179159:0.724947:0.179159:0.708478:0.171203:0.708478:0.000000
:@0.186384:0.722807:0.192799:0.722807:0.192799:0.706989:0.186384:0.706989:0.000000
La pendiente de la recta tangente   a la elipse en el punto   está de-:@0.108244:0.759532:0.595771:0.759532:0.595771:0.743035:0.108244:0.743035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.353279:0.759648:0.361120:0.759648:0.361120:0.743179:0.353279:0.743179:0.000000
u:@0.526011:0.759648:0.535220:0.759648:0.535220:0.743179:0.526011:0.743179:0.000000
:@0.528381:0.760024:0.534796:0.760024:0.534796:0.744206:0.528381:0.744206:0.000000
finida como: :@0.108244:0.776883:0.201178:0.776883:0.201178:0.760385:0.108244:0.760385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m = –              , entonces   = –                    = –       .:@0.108244:0.811585:0.470893:0.811585:0.470893:0.795087:0.108244:0.795087:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.286467:0.811700:0.301263:0.811700:0.301263:0.795232:0.286467:0.795232:0.000000
La ecuación cartesiana de   es: :@0.108244:0.860543:0.327691:0.860543:0.327691:0.844045:0.108244:0.844045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.294152:0.860658:0.301993:0.860658:0.301993:0.844190:0.294152:0.844190:0.000000
( ,  )     tal que   +        = –        (  + 2).:@0.108244:0.895244:0.404903:0.895244:0.404903:0.878747:0.108244:0.878747:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.114197:0.895360:0.136256:0.895360:0.136256:0.878891:0.114197:0.878891:0.000000:0.000000:0.000000
:@0.146338:0.894726:0.160991:0.894726:0.160991:0.881352:0.146338:0.881352:0.000000
:@0.165133:0.894157:0.178437:0.894157:0.178437:0.881295:0.165133:0.881295:0.000000
2:@0.178437:0.888892:0.183391:0.888892:0.183391:0.879274:0.178437:0.879274:0.000000
y:@0.240821:0.895360:0.248508:0.895360:0.248508:0.878891:0.240821:0.878891:0.000000
x:@0.361132:0.895360:0.368607:0.895360:0.368607:0.878891:0.361132:0.878891:0.000000
En la Figura 2.34. se muestran la elipse  (0, 4, 1), el punto    –2, –       :@0.108237:0.929946:0.583800:0.929946:0.583800:0.913448:0.108237:0.913448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E:@0.378912:0.930061:0.386869:0.930061:0.386869:0.913593:0.378912:0.913593:0.000000
:@0.394095:0.927921:0.400510:0.927921:0.400510:0.912103:0.394095:0.912103:0.000000
y la recta tangente.:@0.108237:0.947296:0.242321:0.947296:0.242321:0.930799:0.108237:0.930799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.307322:0.406507:0.314797:0.406507:0.314797:0.390039:0.307322:0.390039:0.000000
0:@0.314797:0.407782:0.319750:0.407782:0.319750:0.398164:0.314797:0.398164:0.000000
a:@0.309047:0.422852:0.318025:0.422852:0.318025:0.406384:0.309047:0.406384:0.000000
x:@0.373459:0.342365:0.380934:0.342365:0.380934:0.325896:0.373459:0.325896:0.000000
a:@0.372707:0.358704:0.381685:0.358704:0.381685:0.342235:0.372707:0.342235:0.000000
x:@0.256390:0.650542:0.263864:0.650542:0.263864:0.634073:0.256390:0.634073:0.000000
a:@0.255638:0.666881:0.264616:0.666881:0.264616:0.650412:0.255638:0.650412:0.000000
y:@0.299840:0.650542:0.307527:0.650542:0.307527:0.634073:0.299840:0.634073:0.000000
b:@0.299050:0.666881:0.308317:0.666881:0.308317:0.650412:0.299050:0.650412:0.000000
y:@0.358291:0.406507:0.365978:0.406507:0.365978:0.390039:0.358291:0.390039:0.000000
0:@0.365979:0.407782:0.370932:0.407782:0.370932:0.398164:0.365979:0.398164:0.000000
b:@0.359978:0.422852:0.369245:0.422852:0.369245:0.406384:0.359978:0.406384:0.000000
y:@0.419890:0.342365:0.427576:0.342365:0.427576:0.325896:0.419890:0.325896:0.000000
b:@0.419100:0.358704:0.428366:0.358704:0.428366:0.342235:0.419100:0.342235:0.000000
  3:@0.408270:0.532370:0.425050:0.532370:0.425050:0.515872:0.408270:0.515872:0.000000:0.000000:0.000000
2:@0.412412:0.548708:0.420908:0.548708:0.420908:0.532210:0.412412:0.532210:0.000000
2:@0.328070:0.400523:0.333023:0.400523:0.333023:0.390905:0.328070:0.390905:0.000000
2:@0.390540:0.336382:0.395493:0.336382:0.395493:0.326764:0.390540:0.326764:0.000000
2:@0.272495:0.644559:0.277449:0.644559:0.277449:0.634941:0.272495:0.634941:0.000000
2:@0.316052:0.644559:0.321005:0.644559:0.321005:0.634941:0.316052:0.634941:0.000000
2:@0.406702:0.679213:0.411656:0.679213:0.411656:0.669595:0.406702:0.669595:0.000000
2:@0.479326:0.679213:0.484279:0.679213:0.484279:0.669595:0.479326:0.669595:0.000000
2:@0.379140:0.400523:0.384093:0.400523:0.384093:0.390905:0.379140:0.390905:0.000000
2:@0.438263:0.336382:0.443216:0.336382:0.443216:0.326764:0.438263:0.326764:0.000000
  3:@0.303561:0.591537:0.320341:0.591537:0.320341:0.575039:0.303561:0.575039:0.000000:0.000000:0.000000
2:@0.307703:0.607875:0.316199:0.607875:0.316199:0.591378:0.307703:0.591378:0.000000
2:@0.390291:0.686256:0.398787:0.686256:0.398787:0.669758:0.390291:0.669758:0.000000
4:@0.390291:0.702594:0.398787:0.702594:0.398787:0.686097:0.390291:0.686097:0.000000
1:@0.342949:0.804857:0.351445:0.804857:0.351445:0.788359:0.342949:0.788359:0.000000
4:@0.342949:0.821195:0.351445:0.821195:0.351445:0.804698:0.342949:0.804698:0.000000
–2:@0.378603:0.804857:0.397599:0.804857:0.397599:0.788359:0.378603:0.788359:0.000000:0.000000
  3:@0.285041:0.686070:0.301821:0.686070:0.301821:0.669572:0.285041:0.669572:0.000000:0.000000:0.000000
2:@0.289183:0.702408:0.297679:0.702408:0.297679:0.685910:0.289183:0.685910:0.000000
  3:@0.452130:0.686256:0.468910:0.686256:0.468910:0.669758:0.452130:0.669758:0.000000:0.000000:0.000000
2:@0.456272:0.702594:0.464768:0.702594:0.464768:0.686097:0.456272:0.686097:0.000000
  3:@0.561226:0.922966:0.578006:0.922966:0.578006:0.906469:0.561226:0.906469:0.000000:0.000000:0.000000
2:@0.565368:0.939305:0.573864:0.939305:0.573864:0.922807:0.565368:0.922807:0.000000
  3:@0.445718:0.804768:0.462499:0.804768:0.462499:0.788270:0.445718:0.788270:0.000000:0.000000:0.000000
2:@0.449860:0.821106:0.458356:0.821106:0.458356:0.804609:0.449860:0.804609:0.000000
  3:@0.387112:0.822499:0.403892:0.822499:0.403892:0.806002:0.387112:0.806002:0.000000:0.000000:0.000000
2:@0.391254:0.838838:0.399750:0.838838:0.399750:0.822340:0.391254:0.822340:0.000000
b:@0.161132:0.804795:0.170399:0.804795:0.170399:0.788326:0.161132:0.788326:0.000000
a:@0.161286:0.821134:0.170264:0.821134:0.170264:0.804665:0.161286:0.804665:0.000000
2:@0.178710:0.798255:0.183664:0.798255:0.183664:0.788637:0.178710:0.788637:0.000000
2:@0.359439:0.798255:0.364392:0.798255:0.364392:0.788637:0.359439:0.788637:0.000000
x:@0.190357:0.804795:0.197832:0.804795:0.197832:0.788326:0.190357:0.788326:0.000000
0:@0.197832:0.806070:0.202785:0.806070:0.202785:0.796452:0.197832:0.796452:0.000000
y:@0.190251:0.821140:0.197938:0.821140:0.197938:0.804671:0.190251:0.804671:0.000000
0:@0.197937:0.823044:0.202890:0.823044:0.202890:0.813426:0.197937:0.813426:0.000000
–:@0.371732:0.829932:0.382231:0.829932:0.382231:0.813435:0.371732:0.813435:0.000000
  3:@0.275141:0.888060:0.291921:0.888060:0.291921:0.871562:0.275141:0.871562:0.000000:0.000000:0.000000
2:@0.279283:0.904399:0.287779:0.904399:0.287779:0.887901:0.279283:0.887901:0.000000
  3:@0.332099:0.888060:0.348879:0.888060:0.348879:0.871562:0.332099:0.871562:0.000000:0.000000:0.000000
12:@0.331983:0.904399:0.348975:0.904399:0.348975:0.887901:0.331983:0.887901:0.000000:0.000000
p:@0.629006:0.267439:0.640487:0.267439:0.640487:0.257415:0.629006:0.257415:0.000000
 :@0.640487:0.268147:0.643368:0.268147:0.643368:0.256670:0.640487:0.256670:0.000000
Figura 2.33.:@0.643368:0.268147:0.697847:0.268147:0.697847:0.256670:0.643368:0.256670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–b:@0.705938:0.246353:0.719836:0.246353:0.719836:0.234876:0.705938:0.234876:0.000000:0.000000
b:@0.726644:0.113864:0.733238:0.113864:0.733238:0.102387:0.726644:0.102387:0.000000
L:@0.795058:0.235801:0.801876:0.235801:0.801876:0.221480:0.795058:0.221480:0.000000
L:@0.663099:0.242791:0.669917:0.242791:0.669917:0.228470:0.663099:0.228470:0.000000
4:@0.669922:0.245544:0.674230:0.245544:0.674230:0.237181:0.669922:0.237181:0.000000
L:@0.661429:0.156041:0.668247:0.156041:0.668247:0.141720:0.661429:0.141720:0.000000
2:@0.668247:0.158790:0.672554:0.158790:0.672554:0.150427:0.668247:0.150427:0.000000
L:@0.659754:0.117065:0.666572:0.117065:0.666572:0.102744:0.659754:0.102744:0.000000
1:@0.666572:0.119814:0.670879:0.119814:0.670879:0.111450:0.666572:0.111450:0.000000
L:@0.686636:0.102388:0.693455:0.102388:0.693455:0.088068:0.686636:0.088068:0.000000
3:@0.693455:0.105138:0.697762:0.105138:0.697762:0.096774:0.693455:0.096774:0.000000
a:@0.770859:0.189383:0.776314:0.189383:0.776314:0.177907:0.770859:0.177907:0.000000
–a:@0.661901:0.189383:0.674660:0.189383:0.674660:0.177907:0.661901:0.177907:0.000000:0.000000
0:@0.712003:0.188842:0.719021:0.188842:0.719021:0.175214:0.712003:0.175214:0.000000
y:@0.709281:0.100203:0.715743:0.100203:0.715743:0.086575:0.709281:0.086575:0.000000
x:@0.837841:0.190108:0.844446:0.190108:0.844446:0.176480:0.837841:0.176480:0.000000
u:@0.731214:0.166565:0.739502:0.166565:0.739502:0.151743:0.731214:0.151743:0.000000
:@0.733434:0.166903:0.739208:0.166903:0.739208:0.152667:0.733434:0.152667:0.000000
E 0:@0.638957:0.222957:0.656160:0.222957:0.656160:0.210069:0.638957:0.210069:0.000000:0.000000:0.000000
( , a, b):@0.645184:0.222867:0.686164:0.222867:0.686164:0.209955:0.645184:0.209955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.651260:0.221995:0.662206:0.223251:0.662206:0.210872:0.651260:0.209616:0.000000:0.000000:0.000000
p:@0.629006:0.911269:0.640487:0.911269:0.640487:0.901245:0.629006:0.901245:0.000000
 :@0.640487:0.911977:0.643368:0.911977:0.643368:0.900500:0.640487:0.900500:0.000000
Figura 2.34.:@0.643368:0.911977:0.697847:0.911977:0.697847:0.900500:0.643368:0.900500:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–1:@0.748900:0.874408:0.762114:0.874408:0.762114:0.862931:0.748900:0.862931:0.000000:0.000000
1:@0.745710:0.832806:0.751621:0.832806:0.751621:0.821329:0.745710:0.821329:0.000000
L:@0.830821:0.891465:0.837639:0.891465:0.837639:0.877145:0.830821:0.877145:0.000000
4:@0.843817:0.867342:0.849728:0.867342:0.849728:0.855865:0.843817:0.855865:0.000000
–2:@0.680059:0.867342:0.693274:0.867342:0.693274:0.855865:0.680059:0.855865:0.000000:0.000000
–4:@0.626706:0.867342:0.639921:0.867342:0.639921:0.855865:0.626706:0.855865:0.000000:0.000000
0:@0.733731:0.866802:0.740749:0.866802:0.740749:0.853173:0.733731:0.853173:0.000000
y:@0.727667:0.808561:0.734129:0.808561:0.734129:0.794932:0.727667:0.794932:0.000000
x:@0.852885:0.868056:0.859489:0.868056:0.859489:0.854427:0.852885:0.854427:0.000000
E 0:@0.800948:0.835992:0.818151:0.835992:0.818151:0.823103:0.800948:0.823103:0.000000:0.000000:0.000000
( , 4, 1):@0.807175:0.835901:0.847552:0.835901:0.847552:0.822990:0.807175:0.822990:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.813251:0.835030:0.824197:0.836286:0.824197:0.823907:0.813251:0.822651:0.000000:0.000000:0.000000
–:@0.347673:0.441903:0.358173:0.441903:0.358173:0.425405:0.347673:0.425405:0.000000
b x:@0.358173:0.442019:0.379866:0.442019:0.379866:0.425550:0.358173:0.425550:0.000000:0.000000:0.000000
2:@0.367440:0.435551:0.372393:0.435551:0.372393:0.425933:0.367440:0.425933:0.000000
0:@0.379866:0.443295:0.384820:0.443295:0.384820:0.433677:0.379866:0.433677:0.000000
a y:@0.352962:0.458364:0.374579:0.458364:0.374579:0.441895:0.352962:0.441895:0.000000:0.000000:0.000000
2:@0.361938:0.451896:0.366891:0.451896:0.366891:0.442278:0.361938:0.442278:0.000000
0:@0.374578:0.461526:0.379531:0.461526:0.379531:0.451908:0.374578:0.451908:0.000000
–b:@0.309543:0.476923:0.328847:0.476923:0.328847:0.460454:0.309543:0.460454:0.000000:0.000000
a:@0.314706:0.493261:0.323684:0.493261:0.323684:0.476792:0.314706:0.476792:0.000000
x:@0.348900:0.476923:0.356375:0.476923:0.356375:0.460454:0.348900:0.460454:0.000000
0:@0.356375:0.478198:0.361328:0.478198:0.361328:0.468579:0.356375:0.468579:0.000000
y:@0.348794:0.493267:0.356481:0.493267:0.356481:0.476799:0.348794:0.476799:0.000000
0:@0.356480:0.496428:0.361433:0.496428:0.361433:0.486810:0.356480:0.486810:0.000000
2:@0.336103:0.470938:0.341056:0.470938:0.341056:0.461320:0.336103:0.461320:0.000000
Competencia :@0.684804:0.313208:0.782426:0.313208:0.782426:0.297736:0.684804:0.297736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.684804:0.325776:0.768866:0.325776:0.768866:0.310304:0.684804:0.310304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Otra forma de presen-:@0.685042:0.350251:0.830247:0.350251:0.830247:0.335188:0.685042:0.335188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tar la ecuación canónica de la :@0.638498:0.366093:0.834572:0.366093:0.834572:0.351030:0.638498:0.351030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
elipse es::@0.638498:0.381935:0.694505:0.381935:0.694505:0.366872:0.638498:0.366872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Forma ordinaria o canónica de :@0.638498:0.404906:0.840834:0.404906:0.840834:0.389843:0.638498:0.389843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la elipse  (0, 0):@0.638498:0.420748:0.734872:0.420748:0.734872:0.405685:0.638498:0.405685:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.693026:0.420853:0.702190:0.420853:0.702190:0.405817:0.693026:0.405817:0.000000
Eje mayor eje  ::@0.638498:0.443718:0.737388:0.443718:0.737388:0.428655:0.638498:0.428655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.728047:0.443824:0.734872:0.443824:0.734872:0.428787:0.728047:0.428787:0.000000
 :@0.638498:0.490452:0.642280:0.490452:0.642280:0.475389:0.638498:0.475389:0.000000
x:@0.647468:0.468438:0.654618:0.468438:0.654618:0.452685:0.647468:0.452685:0.000000
2:@0.655792:0.460636:0.660502:0.460636:0.660502:0.451490:0.655792:0.451490:0.000000
a:@0.646893:0.487769:0.655480:0.487769:0.655480:0.472016:0.646893:0.472016:0.000000
2:@0.655582:0.479967:0.660292:0.479967:0.660292:0.470821:0.655582:0.470821:0.000000
+:@0.665373:0.477382:0.675489:0.477382:0.675489:0.461809:0.665373:0.461809:0.000000
y:@0.680133:0.468434:0.687486:0.468434:0.687486:0.452681:0.680133:0.452681:0.000000
2:@0.688459:0.460636:0.693169:0.460636:0.693169:0.451490:0.688459:0.451490:0.000000
b:@0.679036:0.487769:0.687899:0.487769:0.687899:0.472016:0.679036:0.472016:0.000000
2:@0.688146:0.479967:0.692856:0.479967:0.692856:0.470821:0.688146:0.470821:0.000000
=:@0.699191:0.477382:0.709307:0.477382:0.709307:0.461809:0.699191:0.461809:0.000000
1:@0.710966:0.476774:0.719092:0.476774:0.719092:0.460993:0.710966:0.460993:0.000000
Eje mayor eje  ::@0.638503:0.513414:0.737586:0.513414:0.737586:0.498351:0.638503:0.498351:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.728052:0.513520:0.735071:0.513520:0.735071:0.498483:0.728052:0.498483:0.000000
 :@0.638503:0.560148:0.642285:0.560148:0.642285:0.545085:0.638503:0.545085:0.000000
y:@0.647834:0.538135:0.655187:0.538135:0.655187:0.522382:0.647834:0.522382:0.000000
2:@0.656159:0.530333:0.660868:0.530333:0.660868:0.521187:0.656159:0.521187:0.000000
a:@0.647102:0.557466:0.655690:0.557466:0.655690:0.541713:0.647102:0.541713:0.000000
2:@0.655792:0.549664:0.660502:0.549664:0.660502:0.540518:0.655792:0.540518:0.000000
+:@0.665739:0.547079:0.675856:0.547079:0.675856:0.531506:0.665739:0.531506:0.000000
x:@0.680131:0.538131:0.687281:0.538131:0.687281:0.522378:0.680131:0.522378:0.000000
2:@0.688459:0.530333:0.693169:0.530333:0.693169:0.521187:0.688459:0.521187:0.000000
b:@0.679193:0.557466:0.688057:0.557466:0.688057:0.541713:0.679193:0.541713:0.000000
2:@0.688302:0.549664:0.693011:0.549664:0.693011:0.540518:0.688302:0.540518:0.000000
=:@0.699191:0.547079:0.709307:0.547079:0.709307:0.531506:0.699191:0.531506:0.000000
1:@0.710966:0.546471:0.719092:0.546471:0.719092:0.530690:0.710966:0.530690:0.000000
Ecuación canónica de la elipse :@0.638503:0.583112:0.838164:0.583112:0.838164:0.568049:0.638503:0.568049:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
con  ( ,  ):@0.638503:0.598954:0.709338:0.598954:0.709338:0.583891:0.638503:0.583891:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C h k:@0.666894:0.599059:0.703903:0.599059:0.703903:0.584023:0.666894:0.584023:0.000000:0.000000:0.000000:0.000000:0.000000
Eje mayor paralelo al eje  ::@0.638503:0.621925:0.807049:0.621925:0.807049:0.606861:0.638503:0.606861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.797709:0.622030:0.804534:0.622030:0.804534:0.606993:0.797709:0.606993:0.000000
 :@0.638503:0.672421:0.642285:0.672421:0.642285:0.657358:0.638503:0.657358:0.000000
x h:@0.653907:0.648962:0.684995:0.648962:0.684995:0.633209:0.653907:0.633209:0.000000:0.000000:0.000000
−:@0.663803:0.649460:0.673920:0.649460:0.673920:0.633887:0.663803:0.633887:0.000000
(:@0.646369:0.652278:0.652505:0.652278:0.652505:0.631566:0.646369:0.631566:0.000000
) (:@0.685159:0.652278:0.720562:0.652278:0.720562:0.631566:0.685159:0.631566:0.000000:0.000000:0.000000
2:@0.691548:0.638843:0.696258:0.638843:0.696258:0.629697:0.691548:0.629697:0.000000
a:@0.664796:0.669747:0.673384:0.669747:0.673384:0.653994:0.664796:0.653994:0.000000
2:@0.673487:0.661946:0.678197:0.661946:0.678197:0.652800:0.673487:0.652800:0.000000
+:@0.701129:0.659361:0.711246:0.659361:0.711246:0.643788:0.701129:0.643788:0.000000
y k:@0.722339:0.648961:0.752321:0.648961:0.752321:0.633208:0.722339:0.633208:0.000000:0.000000:0.000000
−:@0.732235:0.649459:0.742351:0.649459:0.742351:0.633886:0.732235:0.633886:0.000000
):@0.753160:0.652278:0.759297:0.652278:0.759297:0.631566:0.753160:0.631566:0.000000
2:@0.759553:0.638843:0.764263:0.638843:0.764263:0.629697:0.759553:0.629697:0.000000
b:@0.732434:0.669747:0.741298:0.669747:0.741298:0.653994:0.732434:0.653994:0.000000
2:@0.741544:0.661946:0.746254:0.661946:0.746254:0.652800:0.741544:0.652800:0.000000
=:@0.770284:0.659361:0.780401:0.659361:0.780401:0.643788:0.770284:0.643788:0.000000
1:@0.782063:0.658753:0.790190:0.658753:0.790190:0.642972:0.782063:0.642972:0.000000
Eje mayor paralelo al eje  ::@0.638503:0.695392:0.807243:0.695392:0.807243:0.680329:0.638503:0.680329:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.797709:0.695498:0.804727:0.695498:0.804727:0.680461:0.797709:0.680461:0.000000
 :@0.638503:0.745889:0.642285:0.745889:0.642285:0.730826:0.638503:0.730826:0.000000
y k:@0.654274:0.722431:0.684256:0.722431:0.684256:0.706679:0.654274:0.706679:0.000000:0.000000:0.000000
−:@0.664170:0.722929:0.674286:0.722929:0.674286:0.707356:0.664170:0.707356:0.000000
(:@0.646369:0.725747:0.652505:0.725747:0.652505:0.705035:0.646369:0.705035:0.000000
) (:@0.685104:0.725747:0.720510:0.725747:0.720510:0.705035:0.685104:0.705035:0.000000:0.000000:0.000000
2:@0.691496:0.712312:0.696206:0.712312:0.696206:0.703167:0.691496:0.703167:0.000000
a:@0.664744:0.743216:0.673332:0.743216:0.673332:0.727463:0.664744:0.727463:0.000000
2:@0.673434:0.735415:0.678144:0.735415:0.678144:0.726270:0.673434:0.726270:0.000000
+:@0.701075:0.732830:0.711192:0.732830:0.711192:0.717258:0.701075:0.717258:0.000000
x h:@0.721917:0.722430:0.753004:0.722430:0.753004:0.706677:0.721917:0.706677:0.000000:0.000000:0.000000
−:@0.731813:0.722928:0.741929:0.722928:0.741929:0.707355:0.731813:0.707355:0.000000
):@0.753163:0.725747:0.759300:0.725747:0.759300:0.705035:0.753163:0.705035:0.000000
2:@0.759553:0.712312:0.764263:0.712312:0.764263:0.703167:0.759553:0.703167:0.000000
b:@0.732434:0.743216:0.741298:0.743216:0.741298:0.727463:0.732434:0.727463:0.000000
2:@0.741544:0.735415:0.746254:0.735415:0.746254:0.726270:0.741544:0.726270:0.000000
=:@0.770284:0.732830:0.780401:0.732830:0.780401:0.717258:0.770284:0.717258:0.000000
1:@0.782063:0.732222:0.790190:0.732222:0.790190:0.716442:0.782063:0.716442:0.000000
 ©:@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