A curve passes through the point (0, -2) and at any point (x, y) of the curve, the product of the slope of its tangent and y-coordinate of the point is equal to the x-coordinate of the point. Find the equation of the curve.

Question

Philoid · Accepted Answer

Given that the product of slope of tangent and y coordinate equals the x-coordinate i.e.,

We have,

⇒

For the curve passes through (0, -2), we get c = 2,

Thus, the required particular solution is:-