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Maths Conic Sections Hyperbola Single Correct MCQ

Published on: August 13, 2026

If P is a point on the rectangular hyperbola x 2 – y 2 = a 2 , C is its centre and S, S ′ are the two foci, then SP. S ′ P =

(CP) 2

(CS) 2

(SS ′ ) 2

Text Solution

Verified by Experts

The correct answer is:

Let the coordinates of P be (x, y)

The eccentricity of the hyperbola is =

So the coordinates of the foci are S(a , 0) and S ′ (–a , 0).

Equation of the corresponding directrices are x = a/ and x = –a/ .

By definition of the hyperbola

SP = e (distance of P from x = a/ )

= | x – a / |

Similarly S ′ P = |x + a/ |

So that SP . S ′ .P = 2 |x 2 – a 2 /2| = 2x 2 – a 2 = x 2 + y 2 = (CP)

2 (  P lies on the hyperbola x

2 – y 2 = a 2 ).

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