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.

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`