Let the circles $C_1:x^2+y^2=16$ and $C_2:{(x-4)}^2+{(y-3)}^2=25$ intersects at points X and Y. Suppose that another circle $C_3:{(x-h)}^2+{(y-k)}^2=r^2$ satisfies following conditions
i) Centre of $C_3$ is collinear with the centres of $C_1$ and  $C_2$
ii) $C_1$ and $C_2$ both lie inside $C_3$ and
iii) $C_3$ touches $C_1$ at M and $C_2$ at N
Let the line through X and Y intersects $C_3$ at Z and W, and let a common tangent of $C_1$ and $C_3$ be a tangent to the parabola $x^2=4\alpha y$