The locus of the mid -point of the portion of the tangents to the ellipse intercepted between the axes is

Question

$\begin{array}{1 1}(A)\;a^2y^2+b^2x^2 =4x^2y^2 \\(B)\;a^2x^2+b^2y^2=4x^2y^2 \\(C)\;x^2+y^2=a^2 \\(D)\;x^2+y^2=b^2 \end{array}$