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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»

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

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


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