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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 values of SPSP is

A
[9,16]
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B
[9,25]
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C
[16,25]
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D
[1,10]
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Solution

The correct option is C [16,25]
Let P(5cosθ,4sinθ) be any point on the ellipse whose e=35
Then
SP=5+5ecosθ
and SP=55ecosθ

SPSP=2525e2cos2θ
So, let f(θ)SPSP=259cos2θ
16f(θ)25

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