Find the locus of the point of intersection of two perpendicular tangents to a given circle $x^2+y^2=a^2$?

Question

$\begin{array}{1 1}(a)\;x^2+y^2=2a^2\\(b)\;x^2+y^2=a^2\\(c)\;x+y=a^2\\(d)\;2x^2+2y^2=3a^2\end{array}$