Question

If $x=aco{s}^{4}t,y=bsi{n}^{4}t$ then $\frac{dy}{dx}$ at $t=\frac{\pi }{4}$ is

• A. $-b/a$
• B. $b/a$
• C. $a/b$
• D. $-a/b$

Answer 1

The correct option is A $-b/a$

Given,

$x=a{\cos }^{4}t$

$\frac{dx}{dt}=-4a{\cos }^3\left(t\right)\sin \left(t\right)$

$y=b{\sin }^{4}t$

$\frac{dy}{dt}=4b{\sin }^{3}t\cos t$

$\frac{dy}{dx}=\frac{4b{\sin }^{3}t\cos t}{-4a{\cos }^{3}t\sin t}$

$=-\frac{b}{a}{\tan }^{2}t$

${\frac{dy}{dx}}_{t=\frac{\pi }{4}}=-\frac{b}{a}{\tan }^2\left(\frac{\pi }{4}\right)$

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