If a circle and the rectangular hyperbola xy = c 2 meet in …

Maths Conic Sections General More Than One Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

If a circle and the rectangular hyperbola xy = c 2 meet in the four points t 1 , t 2 , t 3 & t 4, then

t 1 t 2 t 3 t 4 = 1

The arthmetic mean of the four points bisects the distance between the centres of the two curves.

The geometrical mean of the four points bisects the distance between the centres of the two curves.

the centre of the circle through the points t 1 , t 2 & t 3 is :

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

(a,b,d)Let the equation of the circle is

x 2 + y 2 + 2gx + 2fy + k = 0

and the equation of the rectangular hyperbola is xy = c 2

put x = ct and y =

c 2 t 2 + + 2gct + + k = 0

c 2 t 4 + 2gct 3 + kt 2 + 2fct + c 2 = 0

t 1 t 2 t 3 t 4 = = 1

A.M. of 4 points is

mid-point of centre of circle (–g, – f) and hyperbola (0, 0) is

Centre of circle is (–g, –f)

t 1 t 2 t 3 t 4 = 1

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