# A rectangular hyperbola whose cetre is C is cut by any circle of radius r in four points $P,Q,R$ and S. Then $CP^2+CQ^2+CR2+CS^2$ is equal to.

$\begin{array}{1 1}(A)\;r^2 \\(B)\;2r^2 \\(C)\;3\;r^2 \\(D)\;4\;r^2 \end{array}$

let the equation of the rectangular hyperbola be $xy=c^2$-----(1)
and equation of circle be $x^2+y^2=r^2$------(2)
Put $y= \large\frac{c^2}{x}$ in (2) we get,