Mathematics

Problem

If two points

P

and

Q

on the hyperbola

\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1

whose centre is

C

, are such that

CP

is perpendicular to

CQ

a < b

, then prove that

\frac{1}{(CP)^2} + \frac{1}{(CQ)^2} = \frac{1}{a^2} - \frac{1}{b^2}