92:@0.058194:0.966765:0.075166:0.966765:0.075166:0.950778:0.058194:0.950778:0.000000:0.000000
Ejercicio resuelto:@0.404236:0.107262:0.522215:0.107262:0.522215:0.090475:0.404236:0.090475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Los focos de una elipse  (0,  ,  ) son   = (–4, 0),    = (4, 0), y los vér-:@0.404236:0.124237:0.891771:0.124237:0.891771:0.107739:0.404236:0.107739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E:@0.571900:0.124353:0.579856:0.124353:0.579856:0.107884:0.571900:0.107884:0.000000
:@0.587044:0.122213:0.593460:0.122213:0.593460:0.106395:0.587044:0.106395:0.000000
a b:@0.600395:0.124353:0.625671:0.124353:0.625671:0.107884:0.600395:0.107884:0.000000:0.000000:0.000000
F:@0.665876:0.124353:0.673428:0.124353:0.673428:0.107884:0.665876:0.107884:0.000000
:@0.668016:0.122213:0.674431:0.122213:0.674431:0.106395:0.668016:0.106395:0.000000
1:@0.672888:0.127515:0.677841:0.127515:0.677841:0.117897:0.672888:0.117897:0.000000
F:@0.754941:0.124353:0.762493:0.124353:0.762493:0.107884:0.754941:0.107884:0.000000
:@0.757060:0.122213:0.763475:0.122213:0.763475:0.106395:0.757060:0.106395:0.000000
2:@0.761940:0.127515:0.766893:0.127515:0.766893:0.117897:0.761940:0.117897:0.000000
tices son (–5, 0), (5, 0). Mostrar que la elipse es::@0.404245:0.141588:0.735640:0.141588:0.735640:0.125090:0.404245:0.125090:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E:@0.488607:0.176405:0.496564:0.176405:0.496564:0.159936:0.488607:0.159936:0.000000
(0, 5, 3) =     = ( ,  )     |         +         = 1   .:@0.496564:0.176289:0.807405:0.176289:0.807405:0.159792:0.496564:0.159792:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.503788:0.174265:0.510203:0.174265:0.510203:0.158447:0.503788:0.158447:0.000000
x:@0.572681:0.176405:0.580156:0.176405:0.580156:0.159936:0.572681:0.159936:0.000000
:@0.574376:0.176781:0.580791:0.176781:0.580791:0.160963:0.574376:0.160963:0.000000
x y:@0.605066:0.176405:0.627124:0.176405:0.627124:0.159936:0.605066:0.159936:0.000000:0.000000:0.000000
:@0.637212:0.175771:0.651864:0.175771:0.651864:0.162397:0.637212:0.162397:0.000000
:@0.656006:0.175202:0.669311:0.175202:0.669311:0.162340:0.656006:0.162340:0.000000
2:@0.669311:0.169938:0.674264:0.169938:0.674264:0.160319:0.669311:0.160319:0.000000
En primer lugar, de las coordenadas de los focos se obtiene   = 4, y de :@0.404241:0.210991:0.895981:0.210991:0.895981:0.194493:0.404241:0.194493:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.821502:0.211106:0.828687:0.211106:0.828687:0.194638:0.821502:0.194638:0.000000
las coordenadas de los vértices,   = 5. Como   =   –  , entonces, :@0.404241:0.228342:0.878641:0.228342:0.878641:0.211844:0.404241:0.211844:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.629119:0.228457:0.638096:0.228457:0.638096:0.211988:0.629119:0.211988:0.000000
c:@0.721727:0.228457:0.728913:0.228457:0.728913:0.211988:0.721727:0.211988:0.000000
2:@0.728906:0.221990:0.733859:0.221990:0.733859:0.212372:0.728906:0.212372:0.000000
a:@0.752952:0.228457:0.761929:0.228457:0.761929:0.211988:0.752952:0.211988:0.000000
2:@0.761928:0.221990:0.766882:0.221990:0.766882:0.212372:0.761928:0.212372:0.000000
b:@0.785666:0.228457:0.794932:0.228457:0.794932:0.211988:0.785666:0.211988:0.000000
2:@0.794931:0.221990:0.799884:0.221990:0.799884:0.212372:0.794931:0.212372:0.000000
b:@0.559781:0.263159:0.569048:0.263159:0.569048:0.246690:0.559781:0.246690:0.000000
2:@0.569043:0.256691:0.573996:0.256691:0.573996:0.247073:0.569043:0.247073:0.000000
 =   –  ,   25 – 16 = 9,:@0.573997:0.263043:0.736232:0.263043:0.736232:0.246545:0.573997:0.246545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.593088:0.263159:0.602066:0.263159:0.602066:0.246690:0.593088:0.246690:0.000000
2:@0.602065:0.256691:0.607018:0.256691:0.607018:0.247073:0.602065:0.247073:0.000000
c:@0.625803:0.263159:0.632988:0.263159:0.632988:0.246690:0.625803:0.246690:0.000000
2:@0.632987:0.256691:0.637940:0.256691:0.637940:0.247073:0.632987:0.247073:0.000000
donde   = 3. La ecuación cartesiana de la elipse   es::@0.404234:0.297745:0.774163:0.297745:0.774163:0.281247:0.404234:0.281247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b:@0.455267:0.297860:0.464534:0.297860:0.464534:0.281392:0.455267:0.281392:0.000000
E:@0.744649:0.297860:0.752605:0.297860:0.752605:0.281392:0.744649:0.281392:0.000000
( ,  )     tal que          +          = 1.:@0.523852:0.329424:0.772151:0.329429:0.772151:0.312931:0.523852:0.312927:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.529805:0.329540:0.551863:0.329540:0.551863:0.313071:0.529805:0.313071:0.000000:0.000000:0.000000
:@0.561963:0.328910:0.576616:0.328910:0.576616:0.315537:0.561963:0.315537:0.000000
:@0.580758:0.328342:0.594063:0.328342:0.594063:0.315479:0.580758:0.315479:0.000000
2:@0.594063:0.323077:0.599016:0.323077:0.599016:0.313459:0.594063:0.313459:0.000000
Calculamos la excentricidad:   =       =      .:@0.404243:0.373109:0.699021:0.373109:0.699021:0.356611:0.404243:0.356611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
e:@0.609244:0.373225:0.616662:0.373225:0.616662:0.356756:0.609244:0.356756:0.000000
Problemas relativos a la elipse:@0.404236:0.433683:0.643294:0.433683:0.643294:0.416001:0.404236:0.416001:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ecuación cartesiana de la recta tangente a una elipse:@0.404236:0.451532:0.807532:0.451532:0.807532:0.434091:0.404236:0.434091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tratamos el problema de hallar la ecuación vectorial o cartesiana de la :@0.404236:0.468496:0.895959:0.468496:0.895959:0.451998:0.404236:0.451998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
recta tangente a una elipse en un punto dado de esta. Para el efecto, :@0.404236:0.485847:0.895859:0.485847:0.895859:0.469349:0.404236:0.469349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
supongamos conocida la elipse  (0,  ,  ), donde  ,      , y un punto :@0.404236:0.503198:0.895906:0.503198:0.895906:0.486700:0.404236:0.486700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
E:@0.627287:0.503313:0.635244:0.503313:0.635244:0.486845:0.627287:0.486845:0.000000
:@0.642470:0.501173:0.648886:0.501173:0.648886:0.485355:0.642470:0.485355:0.000000
a b:@0.654973:0.503313:0.679402:0.503313:0.679402:0.486845:0.654973:0.486845:0.000000:0.000000:0.000000
a b:@0.741858:0.503313:0.766288:0.503313:0.766288:0.486845:0.741858:0.486845:0.000000:0.000000:0.000000
:@0.769732:0.502679:0.784384:0.502679:0.784384:0.489306:0.769732:0.489306:0.000000
:@0.787816:0.502111:0.801121:0.502111:0.801121:0.489249:0.787816:0.489249:0.000000
+:@0.801121:0.496846:0.807421:0.496846:0.807421:0.487228:0.801121:0.487228:0.000000
de esta   = ( ,  )    (0,  ,  ).:@0.404238:0.520548:0.615819:0.520548:0.615819:0.504051:0.404238:0.504051:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.458795:0.520664:0.468004:0.520664:0.468004:0.504195:0.458795:0.504195:0.000000
:@0.461263:0.521040:0.467678:0.521040:0.467678:0.505222:0.461263:0.505222:0.000000
x y:@0.492723:0.520664:0.519731:0.520664:0.519731:0.504195:0.492723:0.504195:0.000000:0.000000:0.000000
0:@0.500194:0.523826:0.505147:0.523826:0.505147:0.514208:0.500194:0.514208:0.000000
0:@0.519731:0.523826:0.524684:0.523826:0.524684:0.514208:0.519731:0.514208:0.000000
:@0.534778:0.520030:0.549430:0.520030:0.549430:0.506656:0.534778:0.506656:0.000000
E:@0.553573:0.520664:0.561529:0.520664:0.561529:0.504195:0.553573:0.504195:0.000000
:@0.568754:0.518524:0.575169:0.518524:0.575169:0.502706:0.568754:0.502706:0.000000
a b:@0.581970:0.520664:0.607111:0.520664:0.607111:0.504195:0.581970:0.504195:0.000000:0.000000:0.000000
Buscamos una recta   tangente a  (0,  ,  ) en el punto:@0.404229:0.555250:0.788127:0.555250:0.788127:0.538752:0.404229:0.538752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.551182:0.555366:0.559023:0.555366:0.559023:0.538897:0.551182:0.538897:0.000000
E:@0.642690:0.555366:0.650647:0.555366:0.650647:0.538897:0.642690:0.538897:0.000000
:@0.657875:0.553226:0.664290:0.553226:0.664290:0.537408:0.657875:0.537408:0.000000
a b:@0.671091:0.555366:0.696232:0.555366:0.696232:0.538897:0.671091:0.538897:0.000000:0.000000:0.000000
u:@0.404229:0.572716:0.413437:0.572716:0.413437:0.556248:0.404229:0.556248:0.000000
:@0.406695:0.573092:0.413110:0.573092:0.413110:0.557274:0.406695:0.557274:0.000000
 = ( ,  )    (0,  ,  ). Más aún, buscamos la ecuación cartesiana :@0.413110:0.572601:0.895954:0.572601:0.895954:0.556103:0.413110:0.556103:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.442239:0.572716:0.471290:0.572716:0.471290:0.556248:0.442239:0.556248:0.000000:0.000000:0.000000
0:@0.449712:0.575879:0.454665:0.575879:0.454665:0.566260:0.449712:0.566260:0.000000
0:@0.471286:0.575879:0.476239:0.575879:0.476239:0.566260:0.471286:0.566260:0.000000
:@0.488372:0.572082:0.503024:0.572082:0.503024:0.558709:0.488372:0.558709:0.000000
E:@0.509208:0.572716:0.517164:0.572716:0.517164:0.556248:0.509208:0.556248:0.000000
:@0.524389:0.570576:0.530804:0.570576:0.530804:0.554758:0.524389:0.554758:0.000000
a b:@0.539647:0.572716:0.566830:0.572716:0.566830:0.556248:0.539647:0.556248:0.000000:0.000000:0.000000
o vectorial de dicha tangente  . Esto nos conduce a considerar dos :@0.404250:0.589951:0.895842:0.589951:0.895842:0.573454:0.404250:0.573454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.622526:0.590067:0.630367:0.590067:0.630367:0.573598:0.622526:0.573598:0.000000
casos.:@0.404250:0.607302:0.445630:0.607302:0.445630:0.590804:0.404250:0.590804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En el primero, la recta tangente   a la elipse  (0,  ,  ) en el punto:@0.404250:0.642004:0.858255:0.642004:0.858255:0.625506:0.404250:0.625506:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.629132:0.642119:0.636973:0.642119:0.636973:0.625651:0.629132:0.625651:0.000000
E:@0.712818:0.642119:0.720775:0.642119:0.720775:0.625651:0.712818:0.625651:0.000000
:@0.728003:0.639979:0.734418:0.639979:0.734418:0.624161:0.728003:0.624161:0.000000
a b:@0.741219:0.642119:0.766360:0.642119:0.766360:0.625651:0.741219:0.625651:0.000000:0.000000:0.000000
u:@0.404250:0.659470:0.413459:0.659470:0.413459:0.643001:0.404250:0.643001:0.000000
:@0.406716:0.659846:0.413132:0.659846:0.413132:0.644028:0.406716:0.644028:0.000000
 = (– , 0) es paralela al eje  . Observamos que en este caso no está :@0.413132:0.659354:0.895815:0.659354:0.895815:0.642857:0.413132:0.642857:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.449909:0.659470:0.458887:0.659470:0.458887:0.643001:0.449909:0.643001:0.000000
x:@0.605127:0.659470:0.612602:0.659470:0.612602:0.643001:0.605127:0.643001:0.000000
definida la pendiente de dicha recta. La ecuación vectorial de esta :@0.404250:0.676705:0.895983:0.676705:0.895983:0.660207:0.404250:0.660207:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
recta está definida como::@0.404250:0.694056:0.583529:0.694056:0.583529:0.677558:0.404250:0.677558:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x t:@0.542055:0.728873:0.561782:0.728873:0.561782:0.712404:0.542055:0.712404:0.000000:0.000000:0.000000
:@0.543750:0.729249:0.550165:0.729249:0.550165:0.713431:0.543750:0.713431:0.000000
( ) = (– , 0) +  (0, 1),        .:@0.550165:0.728757:0.753972:0.728757:0.753972:0.712260:0.550165:0.712260:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.603280:0.728873:0.612257:0.728873:0.612257:0.712404:0.603280:0.712404:0.000000
t:@0.652695:0.728873:0.658359:0.728873:0.658359:0.712404:0.652695:0.712404:0.000000
t:@0.709335:0.728873:0.714999:0.728873:0.714999:0.712404:0.709335:0.712404:0.000000
:@0.719118:0.728239:0.733770:0.728239:0.733770:0.714866:0.719118:0.714866:0.000000
:@0.737912:0.727670:0.751217:0.727670:0.751217:0.714808:0.737912:0.714808:0.000000
 :@0.404230:0.746108:0.408372:0.746108:0.408372:0.729611:0.404230:0.729611:0.000000
En la Figura 2.31. se muestra la recta tangente   a la elipse  (0,  ,  ) en :@0.404230:0.763459:0.895899:0.763459:0.895899:0.746961:0.404230:0.746961:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L:@0.727783:0.763575:0.735624:0.763575:0.735624:0.747106:0.727783:0.747106:0.000000
E:@0.810931:0.763575:0.818888:0.763575:0.818888:0.747106:0.810931:0.747106:0.000000
:@0.826159:0.761435:0.832574:0.761435:0.832574:0.745617:0.826159:0.745617:0.000000
a b:@0.839240:0.763575:0.864246:0.763575:0.864246:0.747106:0.839240:0.747106:0.000000:0.000000:0.000000
el punto   = (– , 0). Se tiene  (0,  ,  )     = { }.:@0.404230:0.780810:0.746150:0.780810:0.746150:0.764312:0.404230:0.764312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.468480:0.780925:0.477689:0.780925:0.477689:0.764457:0.468480:0.764457:0.000000
:@0.470946:0.781301:0.477361:0.781301:0.477361:0.765483:0.470946:0.765483:0.000000
a:@0.512906:0.780925:0.521883:0.780925:0.521883:0.764457:0.512906:0.764457:0.000000
E:@0.610311:0.780925:0.618267:0.780925:0.618267:0.764457:0.610311:0.764457:0.000000
:@0.625492:0.778785:0.631907:0.778785:0.631907:0.762967:0.625492:0.762967:0.000000
a b:@0.638708:0.780925:0.663849:0.780925:0.663849:0.764457:0.638708:0.764457:0.000000:0.000000:0.000000
:@0.673944:0.780593:0.689992:0.780593:0.689992:0.765946:0.673944:0.765946:0.000000
L:@0.694134:0.780925:0.701975:0.780925:0.701975:0.764457:0.694134:0.764457:0.000000
u:@0.727694:0.780925:0.736903:0.780925:0.736903:0.764457:0.727694:0.764457:0.000000
:@0.730160:0.781301:0.736575:0.781301:0.736575:0.765483:0.730160:0.765483:0.000000
De manera similar, tratamos el caso de la recta tangente   a  (0,  ,  ) :@0.404230:0.815511:0.895918:0.815511:0.895918:0.799014:0.404230:0.799014:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
L E:@0.807275:0.815627:0.839737:0.815627:0.839737:0.799158:0.807275:0.799158:0.000000:0.000000:0.000000
:@0.846927:0.813487:0.853342:0.813487:0.853342:0.797669:0.846927:0.797669:0.000000
a b:@0.860412:0.815627:0.885823:0.815627:0.885823:0.799158:0.860412:0.799158:0.000000:0.000000:0.000000
en el punto   = (– , 0).:@0.404250:0.832862:0.567696:0.832862:0.567696:0.816364:0.404250:0.816364:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.490192:0.832978:0.499401:0.832978:0.499401:0.816509:0.490192:0.816509:0.000000
:@0.492658:0.833354:0.499073:0.833354:0.499073:0.817535:0.492658:0.817535:0.000000
a:@0.534618:0.832978:0.543595:0.832978:0.543595:0.816509:0.534618:0.816509:0.000000
En el segundo caso, suponemos que ( ,  )    (0,  ,  ) con   ≠ ±   :@0.404250:0.867563:0.895891:0.867563:0.895891:0.851066:0.404250:0.851066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.677693:0.867679:0.705751:0.867679:0.705751:0.851210:0.677693:0.851210:0.000000:0.000000:0.000000
0:@0.685154:0.870841:0.690107:0.870841:0.690107:0.861223:0.685154:0.861223:0.000000
0:@0.705759:0.870841:0.710712:0.870841:0.710712:0.861223:0.705759:0.861223:0.000000
:@0.721875:0.867045:0.736528:0.867045:0.736528:0.853672:0.721875:0.853672:0.000000
E:@0.741730:0.867679:0.749687:0.867679:0.749687:0.851210:0.741730:0.851210:0.000000
:@0.756911:0.865539:0.763326:0.865539:0.763326:0.849721:0.756911:0.849721:0.000000
a b:@0.771187:0.867679:0.797387:0.867679:0.797387:0.851210:0.771187:0.851210:0.000000:0.000000:0.000000
x:@0.840715:0.867679:0.848190:0.867679:0.848190:0.851210:0.840715:0.851210:0.000000
a,:@0.880228:0.867679:0.891749:0.867679:0.891749:0.851210:0.880228:0.851210:0.000000:0.000000
exactamente –  <   <  . En la Figura 2.32. se muestra la recta tangente :@0.404222:0.884914:0.895962:0.884914:0.895962:0.868417:0.404222:0.868417:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a x:@0.508852:0.885030:0.543317:0.885030:0.543317:0.868561:0.508852:0.868561:0.000000:0.000000:0.000000
0:@0.543119:0.888192:0.548072:0.888192:0.548072:0.878574:0.543119:0.878574:0.000000
a:@0.566164:0.885030:0.575142:0.885030:0.575142:0.868561:0.566164:0.868561:0.000000
L:@0.404220:0.902381:0.412061:0.902381:0.412061:0.885912:0.404220:0.885912:0.000000
 a la elipse en el punto   = ( ,  )    (0,  ,  ).:@0.412061:0.902265:0.730889:0.902265:0.730889:0.885767:0.412061:0.885767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
u:@0.573849:0.902381:0.583058:0.902381:0.583058:0.885912:0.573849:0.885912:0.000000
:@0.576317:0.902757:0.582732:0.902757:0.582732:0.886938:0.576317:0.886938:0.000000
x y:@0.607777:0.902381:0.634802:0.902381:0.634802:0.885912:0.607777:0.885912:0.000000:0.000000:0.000000
0:@0.615264:0.905543:0.620218:0.905543:0.620218:0.895925:0.615264:0.895925:0.000000
0:@0.634801:0.905543:0.639754:0.905543:0.639754:0.895925:0.634801:0.895925:0.000000
:@0.649848:0.901746:0.664501:0.901746:0.664501:0.888373:0.649848:0.888373:0.000000
E:@0.668643:0.902381:0.676600:0.902381:0.676600:0.885912:0.668643:0.885912:0.000000
:@0.683824:0.900241:0.690240:0.900241:0.690240:0.884423:0.683824:0.884423:0.000000
a b:@0.697040:0.902381:0.722182:0.902381:0.722182:0.885912:0.697040:0.885912:0.000000:0.000000:0.000000
Competencia digital:@0.199644:0.115710:0.341997:0.115710:0.341997:0.100238:0.199644:0.100238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para conocer más sobre :@0.199880:0.144338:0.358101:0.144338:0.358101:0.129274:0.199880:0.129274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la elipse y la circunferencia, :@0.153337:0.160180:0.330203:0.160180:0.330203:0.145116:0.153337:0.145116:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
visita:@0.153337:0.176444:0.190521:0.176444:0.190521:0.160972:0.153337:0.160972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 esta página::@0.190522:0.176022:0.269766:0.176022:0.269766:0.160958:0.190522:0.160958:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lynk.ec/12m06:@0.153337:0.199322:0.251226:0.199322:0.251226:0.184009:0.153337:0.184009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.143988:0.666358:0.155468:0.666358:0.155468:0.656334:0.143988:0.656334:0.000000
 :@0.155468:0.667066:0.158350:0.667066:0.158350:0.655589:0.155468:0.655589:0.000000
Figura 2.31.:@0.158350:0.667066:0.212828:0.667066:0.212828:0.655589:0.158350:0.655589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.143988:0.906411:0.155468:0.906411:0.155468:0.896386:0.143988:0.896386:0.000000
 :@0.155468:0.907119:0.158350:0.907119:0.158350:0.895642:0.155468:0.895642:0.000000
Figura 2.32.:@0.158350:0.907119:0.212828:0.907119:0.212828:0.895642:0.158350:0.895642:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.696262:0.168852:0.703737:0.168852:0.703737:0.152384:0.696262:0.152384:0.000000
5:@0.695742:0.185075:0.704238:0.185075:0.704238:0.168578:0.695742:0.168578:0.000000
x:@0.670422:0.322867:0.677897:0.322867:0.677897:0.306398:0.670422:0.306398:0.000000
5:@0.669902:0.339090:0.678398:0.339090:0.678398:0.322592:0.669902:0.322592:0.000000
c:@0.641941:0.366195:0.649127:0.366195:0.649127:0.349726:0.641941:0.349726:0.000000
a:@0.641055:0.382533:0.650032:0.382533:0.650032:0.366064:0.641055:0.366064:0.000000
y:@0.744739:0.168852:0.752426:0.168852:0.752426:0.152384:0.744739:0.152384:0.000000
3:@0.744334:0.185075:0.752830:0.185075:0.752830:0.168578:0.744334:0.168578:0.000000
y:@0.718898:0.322867:0.726585:0.322867:0.726585:0.306398:0.718898:0.306398:0.000000
3:@0.718494:0.339090:0.726990:0.339090:0.726990:0.322592:0.718494:0.322592:0.000000
4:@0.680895:0.366079:0.689391:0.366079:0.689391:0.349581:0.680895:0.349581:0.000000
5:@0.680895:0.382418:0.689391:0.382418:0.689391:0.365920:0.680895:0.365920:0.000000
2:@0.712370:0.162866:0.717323:0.162866:0.717323:0.153248:0.712370:0.153248:0.000000
2:@0.686526:0.316883:0.691479:0.316883:0.691479:0.307265:0.686526:0.307265:0.000000
2:@0.760947:0.162866:0.765900:0.162866:0.765900:0.153248:0.760947:0.153248:0.000000
2:@0.735103:0.316883:0.740056:0.316883:0.740056:0.307265:0.735103:0.307265:0.000000
–b:@0.229969:0.637988:0.243867:0.637988:0.243867:0.626512:0.229969:0.626512:0.000000:0.000000
b:@0.235598:0.498368:0.242192:0.498368:0.242192:0.486891:0.235598:0.486891:0.000000
L:@0.190987:0.509895:0.197123:0.509895:0.197123:0.497006:0.190987:0.497006:0.000000
E 0:@0.284857:0.519502:0.302060:0.519502:0.302060:0.506613:0.284857:0.506613:0.000000:0.000000:0.000000
( , a, b):@0.291084:0.519411:0.332064:0.519411:0.332064:0.506500:0.291084:0.506500:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.297160:0.518540:0.308106:0.519796:0.308106:0.507417:0.297160:0.506160:0.000000:0.000000:0.000000
a:@0.296563:0.577454:0.302018:0.577454:0.302018:0.565978:0.296563:0.565978:0.000000
–a:@0.185931:0.577454:0.198689:0.577454:0.198689:0.565978:0.185931:0.565978:0.000000:0.000000
0:@0.236034:0.576913:0.243052:0.576913:0.243052:0.563285:0.236034:0.563285:0.000000
y:@0.233312:0.482827:0.239774:0.482827:0.239774:0.469199:0.233312:0.469199:0.000000
x:@0.353501:0.578179:0.360105:0.578179:0.360105:0.564551:0.353501:0.564551:0.000000
u:@0.218022:0.560942:0.225228:0.560942:0.225228:0.548054:0.218022:0.548054:0.000000
:@0.219951:0.561237:0.224972:0.561237:0.224972:0.548857:0.219951:0.548857:0.000000
–b:@0.215608:0.889767:0.229505:0.889767:0.229505:0.878290:0.215608:0.878290:0.000000:0.000000
b:@0.221236:0.764399:0.227830:0.764399:0.227830:0.752922:0.221236:0.752922:0.000000
L:@0.301281:0.874364:0.308099:0.874364:0.308099:0.860043:0.301281:0.860043:0.000000
E 0:@0.265814:0.767542:0.283018:0.767542:0.283018:0.754653:0.265814:0.754653:0.000000:0.000000:0.000000
( , a, b)     = { }:@0.272041:0.767451:0.367862:0.767451:0.367862:0.754540:0.272041:0.754540:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.278117:0.766580:0.289063:0.767836:0.289063:0.755457:0.278117:0.754201:0.000000:0.000000:0.000000
:@0.316261:0.766980:0.327425:0.766980:0.327425:0.756791:0.316261:0.756791:0.000000
L:@0.330666:0.767542:0.336803:0.767542:0.336803:0.754653:0.330666:0.754653:0.000000
u:@0.356328:0.767542:0.363535:0.767542:0.363535:0.754653:0.356328:0.754653:0.000000
:@0.357504:0.767836:0.362524:0.767836:0.362524:0.755457:0.357504:0.755457:0.000000
a:@0.280528:0.836359:0.285983:0.836359:0.285983:0.824882:0.280528:0.824882:0.000000
–a:@0.171571:0.836359:0.184329:0.836359:0.184329:0.824882:0.171571:0.824882:0.000000:0.000000
0:@0.221674:0.835819:0.228692:0.835819:0.228692:0.822191:0.221674:0.822191:0.000000
y:@0.218952:0.749270:0.225414:0.749270:0.225414:0.735642:0.218952:0.735642:0.000000
x:@0.339141:0.837073:0.345745:0.837073:0.345745:0.823445:0.339141:0.823445:0.000000
u:@0.245909:0.809770:0.254197:0.809770:0.254197:0.794948:0.245909:0.794948:0.000000
:@0.248129:0.810108:0.253903:0.810108:0.253903:0.795872:0.248129:0.795872:0.000000
E 0:@0.150302:0.871191:0.167505:0.871191:0.167505:0.858303:0.150302:0.858303:0.000000:0.000000:0.000000
( , a, b):@0.156529:0.871101:0.197508:0.871101:0.197508:0.858190:0.156529:0.858190:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.162605:0.870230:0.173551:0.871486:0.173551:0.859106:0.162605:0.857850:0.000000:0.000000:0.000000