How many parabolas can be drawn if the two en | vedclass

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(B) Let the two endpoints of the latus rectum be $L_1$ and $L_2$. The length of the latus rectum is $4a$,where $a$ is the distance from the vertex to

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$2$

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(B) Let the two endpoints of the latus rectum be $L_1$ and $L_2$. The length of the latus rectum is $4a$,where $a$ is the distance from the vertex to the focus. Since the latus rectum is perpendicular to the axis of the parabola,the axis must be the perpendicular bisector of the segment $L_1L_2$. There are two possible directions for the parabola to open along this axis (either towards the focus or away from it),resulting in two distinct parabolas.

How many parabolas can be drawn if the two endpoints of the latus rectum are given?

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