Find the equation of the curve that passes through the point (0, a) and is such that at any point (x, y) on it, the product of its slope and the ordinate is equal to the ab.

Question

Philoid · Accepted Answer

Given product of slope of the curve and ordinate = x

⇒

Integrating both sides we have,

⇒ ∫ydy = ∫xdx

⇒ ……(1)

The curve passes through point (0,a)

⇒

Putting the value of c in equation (1)