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

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