Find the locus of mid-points of the portions of the tangents to the ellipse $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}$$=1$ intercepted between the axis?

Question

$\begin{array}{1 1}(a)\;a^2y^2+b^2x^2=4x^2y^2\\(b)\;a^2+b^2=4x^2y^2\\(c)\;a^2y^2+b^2x^2=2x^2y^2\\(d)\;\text{None of these}\end{array}$