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Question

If S and S are the foci of the ellipse x225+y216=1 and P is any point on it, then range of value of SPSP is:

A
9f(θ)16
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B
9f(θ)25
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C
16f(θ)25
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D
1f(θ)16
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Solution

The correct option is C 16f(θ)25
Let P(5cosθ,4sinθ) be any point on the ellipse in parametric form
Then SP=5+5ecosθ
SP=55ecosθ
where, e is the eccentricity of the ellipse
Now,
(SPSP)(SP+SP)=2525e2cos2θ
=25sin2θ+16cos2θ
16f(θ)25
Hence, option C.

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