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 :
Answer & explanation
Correct answer: option 1
$\frac{dy}{dx}=\frac{4x}{y}⇒∫ydy=∫4xdx$ (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 $\frac{y^2}{2}=2x^2-6$
$⇒y^2=4x^2-12$