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TRASLACIÓN DE EJES

Debido a que hay cónicas que no tienen su centro en el origen, ni sus ejes coinciden con algún eje coordinado “x” o “y”, la ecuación de la cónica se complica demasiado.

Para simplificar esta ecuación, trasladamos, rotamos o hacemos ambas cosas con los ejes coordenados, para que coincidan con los ejes de la cónica.

De esta manera podemos obtener una ecuación como las que hemos estudiado.

Cuando hacemos alguno movimiento en los ejes tenemos que aplicar los cambios en la ecuación respectiva.

PROCEDIMIENTO PARA TRASLADAR LOS EJES


1.-El origen de los ejes coordenados se trasladan a un nuevo origen O´ (h, k)

2-Por lo tanto, cualquier punto de la gráfica ahora será

                    x = x`+ h

                    y = y´+ k

3.-Estas nuevas coordenadas se sustituyen en la ecuación dada.

4.-Se desarrolla la nueva ecuación hasta simplificarla lo más posible

Ejemplos de traslación de ejes:

1.- Simplifica la siguiente ecuación que representa a una parábola:

         Primero sustituimos las nuevas coordenadas en la ecuación dada:

         Desarrollando tenemos que:

         Igualamos el coeficiente de y’ a cero

         Sustituimos k en el coeficiente independiente para obtener h:

Mas ejemplos, ejercicios y preguntas clave de examen, en nuestras guías digitales.

error: Contenido Protegido !!
Curso para la UNAM

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