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

Question

Philoid · Accepted Answer

Equation of the family of an ellipse having foci on the y-axis and centers at the origin can be represented by

(1)

Differentiating the above equation with respect to x on both sides, we have,

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

Rearranging the above equation

This is the required differential equation.