HYPERBOLA : Problem

Question

If two points $P$ and $Q$ on the hyperbola $\frac{x^2}{a^2} -\frac{y^2}{b^2} = 1$ whose centre is $C(0,0)$ are such that $CP$ is perpendicular to $CQ$ , $a<b$ , then prove that $$\frac{1}{(CP)^2} +\frac{1}{(CQ)^2} = \frac{1}{a^2} -\frac{1}{b^2} $$