Find the equation of the 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.

Explanation

Given, `y*(dy)/(dx)=ximpliesydy=xdx`
`implies intydy=intxdx+cimplies(y^(2))/(2)=(x^(2))/(2)+c`
This curve passes through the point `(0,-2)`.
`(4)/(2)=0+cimpliesc=2`
Therefore, equation of curve is `(y^(2))/(2)=(x^(2))/(2)+2`
`implies y^(2)=x^(2)+4`