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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