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 B749 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+S′Q=2a=10 ⇒S′Q=10−169=749