Find the equation of a curve passing through the point (0, –2) given that at any point (x, y) on 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.

We know that slope of a tangent is =

So we are given that the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.

Now separating variables,

⇒ ydy = xdx

Integrating both sides,

Now the curve passes through (0, -2).

∴ 4-0 = 2c

⇒ c = 2

Putting the value of c in i)

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