Find the equation of director circle for ellipse $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}$$=1$?

Question

$\begin{array}{1 1}(a)\;x^2-y^2=a^2+b^2\\(b)\;x^2+y^2=a^2+b^2\\(c)\;x^2-y^2=a^2-b^2\\(d)\;\text{None of these}\end{array}$