Form the differential equation of the family of ellipses having foci on $y$-axis and centre at origin.

Question

$\begin{array}{1 1}(A)xyy'' -x(y')^2 - yy' = 0 \\(B)\;xyy'' + x(y')^2 - yy' = 0 \\(C)\;xyy'' + x(y')^2 + yy' = 0 \\(D)\;xyy'' + x(y')^2 +y' = 0 \end{array} $