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Question

If normal at P(2,332) meets the major axis of the ellipse x216+y29=1 at Q and S,S are foci of given ellipse along positive and negative directions of axes, then the ratio SQ:SQ is

A
787+8
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B
878+7
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C
7+878
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D
8+787
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Solution

The correct option is B 878+7
Equation of the ellipse is
x216+y29=1.
e=1916=74

Hence, coordinates of foci are S(7,0) and S(7,0).


Normal at P is a bisector of angle between SP and SP
So, applying angular bisector theorem (angular bisector divides opposite side in the ration of its corresponding sides) in SPS
i.e.,SQSQ=SPSP
SQSQ=aex1a+ex1SQSQ=4724+72SQSQ=878+7

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