If a rectangular hyperbola have the equation, $xy = c^2$, prove that the locus of the middle points of the chords of constant length 2d is $(x^2 + y^2)(x y - c^2) = {d^2} xy$.
I tried to apply the same logic of mid point of the contact of contact(h,k) which is applied on circle $x^2+y^2=r^2$ as $hx+ky=h^2+k^2$ but not getting any success.