If polar of the parabola $x^2=4ay$ is always touching the parabola $y^2=4ax$ then locus of the pole is :

Question

$\begin{array}{1 1}(A)\;x-y=2a^2 \\(B)\;xy=-2a^2 \\(C)\;xy=a^2 \\(D)\;none\;of\;these \end{array}$