Form the differential equation of the family of curves y²=m(a²-x²), where a and m are parameters.

Question

Form the differential equation of the family of curves y 2 =m(a 2 -x 2 ), where a and m are parameters.

Philoid · Accepted Answer

Equation of the family of curves, y²=m(a²-x²), where a and m are parameters.

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

(1)

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

(2)

From equations (1) and (2),

This is the required differential equation.

Form the differential equation of the family of curves y2=m(a2-x2), where a and m are parameters.