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Question

If S and S′ are two foci of the ellipse 16x2+25y2=400 and PSQ is a focal chord such that SP=16, then S′Q=

A
169
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B
749
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C
379
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D
323
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Solution

The correct option is B 749
Equation of the ellipse is
x225+y216=1.

We know that if PSQ is a focal chord of ellipse, then length of semi latus rectum is the harmonic mean of SP and SQ.
1SP+1SQ=2ab2
116+1SQ=2×516
1SQ=916
Now SQ+SQ=2a=10
SQ=10169=749

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