Form the differential equation of the family of hyperbolas having foci on the and centers at the origin.

Equation of the family of an ellipse having foci on the -axis and centers at the origin can be represented by
Differentiating the above equation with respect to on both sides, we have,

Again differentiating the above equation with respect to on both sides, we have,

Rearranging the above equation

This is the required differential equation.