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Question

If P is a point on the rectangular hyperbola x2y2=a2, C is its centre and S, and S are the two foci, then SP.SP=


A

2

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B

(CP)2

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C

(CS)2

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D

(SS)2

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Solution

The correct option is B

(CP)2


PS=ex+a=2x+a

PS=exa=2xa [Here, e is eccentricity]

PS×PS=2x2a2

=2x2(x2y2)

=x2+y2=(CP)2


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