Question

Find $\frac{dy}{dx}$, if x=3a^2 cos^2⁡θ and y=4a sin^2⁡θ.

(a) $\frac{3}{4a}$

(b) –$\frac{4}{3a}$

(c) $\frac{4}{3a}$

(d) –$\frac{3}{4a}$

I had been asked this question by my school teacher while I was bunking the class.

My enquiry is from Derivatives of Functions in Parametric Forms topic in division Continuity and Differentiability of Mathematics – Class 12

Answer 1

Right choice is (b) –$\frac{4}{3a}$

Easy explanation: Given that, x=3a^2 cos^2⁡θ and y=4a sin^2⁡θ

Then, $\frac{dx}{dθ}$=3a^2.(2 cos⁡θ)(-sin⁡θ)=-3a^2 sin⁡2θ

$\frac{dy}{dθ}$=4a(2 sin⁡θ)(cos⁡θ)=4a sin⁡2θ

$\frac{dy}{dx}$=$\frac{dy}{dθ}×\frac{dθ}{dx}=-\frac{4a \,sin⁡2θ}{3a^2 \,sin⁡2θ}=-\frac{4}{3a}$