The equation of the curve whose slope is given by $\frac{dy}{dx}=\frac{4x}{y}, x > 0, y> 0$ and which passes through the point (2, 2) is :

$y^2=4x^2-12$ $x^2=4y^2-12$ $y^2=4x^2+12$ $x^2=4y^2+12$

$y^2=4x^2-12$

$\frac{dy}{dx}=\frac{4x}{y}⇒∫ydy=∫4xdx$ (cross multiplying and integrating) so $\frac{y^2}{2}=2x^2+C$ curves passes through (2, 2) so $\frac{2^2}{2}=2×2^2+C⇒2=8+C$ so $C=-6$ so $\frac{y^2}{2}=2x^2-6$ $⇒y^2=4x^2-12$