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$If P S Q and P S^{'} R are two chords of an ellipse through its foci S and S respectively, then \frac{P S}{S Q} + \frac{P S^{'}}{S^{'} R} =$

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a

21+e21−e2

b

1+e21−e2

c

21-e21+e2

d

1-e21+e2

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detailed solution

Correct option is A

We know that semi latus rectum is harmonic mean of the segments of focal chord.∴ 1SP+1SQ=2ab2----(i) and 1S′P+1S′R=2ab2---(ii) Also SP+S′P=2a----(iii) From (i), 1+SPSQ=2ab2SP From (ii), 1+S′PS′R=2ab2S′P On adding, we get 2+SPSQ+S′PS′R=2ab2SP+S′P⇒ 2+SPSQ+S′PS′R=4a2b2=41−e2⇒ SPSQ+S′PS′R=41−e2−2=21+e21−e2

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