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Find the equation of the curve passing through thepoint (0, -2) given that at any point `(x , y)`on the curve the product of the slope of its tangentand `y`coordinate of the point is equal to thex-coordinate of the point.

Answer» Correct Answer - `y^(2)=x^(2)+4`
`y(dy)/(dx) =x rArr inty dy = int x dx rArr (y^(2))/(2) = (x^(2))/(2)+C.`
Put x = 0 and y = 2 to get C = 2.


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