A rectangular hyperbola whose centre is C is cut by any cir…

Maths Conic Sections Hyperbola Single Correct MCQ

Published on: August 13, 2026

A rectangular hyperbola whose centre is C is cut by any circle of radius r in four points P, Q, R and S. then CP 2 + CQ 2 + CR 2 + CS 2 is equal to -

r 2

2r 2

3r 2

4r 2

Text Solution

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The correct answer is:

Let equation of the rectangular hyperbola be

xy = c 2 … (1)

and equation of circle be

x 2 + y 2 = r 2 … (2)

Put y = in equation (2), we get

x 2 + = r 2 ⇒ x 4 – r 2 x 2 + c 4 = 0 … (3)

Now, CP 2 + CQ 2 + CR 2 + CS 2 =

= – 2 Σ x 1 x 2 + – 2 Σ y 1 y 2

= 2r

2 + 2r 2 = 4r 2 . [From (3)]

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