Question

Find $\frac{dy}{dx},$ if $x=b{\sin }^2\theta$ and $y=a{\cos }^2\theta$.

Answer 1

$x=b{\sin }^2\theta$

Differentiating w.r.t. $\theta$, we get,

$\frac{dx}{d\theta }=2b\sin \theta \cos \theta$

$y=a{\cos }^2\theta$

Differentiating w.r.t. $\theta$, we get,

$\frac{dy}{d\theta }=-2a\cos \theta \sin \theta$

Thus, $\frac{dy}{dx}=\frac{-2a\cos \theta \sin \theta }{2b\sin \theta \cos \theta }$

$\frac{dy}{dx}=-\frac{a}{b}$