If x = a cos^3 theta and y = b sin^3 theta,th | vedclass

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Question

(C) Given equations are $x = a \cos^3 	heta$ and $y = b \sin^3 	heta$.Step $1$: Express $\cos 	heta$ and $\sin 	heta$ in terms of $x$ and $y$.$\fr

Vedclass · Accepted Answer

$(\frac{x}{a})^{2/3} + (\frac{y}{b})^{2/3} = 1$

Vedclass · Answer

(C) Given equations are $x = a \cos^3 	heta$ and $y = b \sin^3 	heta$.Step $1$: Express $\cos 	heta$ and $\sin 	heta$ in terms of $x$ and $y$.$\frac{x}{a} = \cos^3 	heta \implies (\frac{x}{a})^{1/3} = \cos 	heta$$\frac{y}{b} = \sin^3 	heta \implies (\frac{y}{b})^{1/3} = \sin 	heta$Step $2$: Use the trigonometric identity $\cos^2 	heta + \sin^2 	heta = 1$.Substituting the expressions from Step $1$:$((\frac{x}{a})^{1/3})^2 + ((\frac{y}{b})^{1/3})^2 = 1$$(\frac{x}{a})^{2/3} + (\frac{y}{b})^{2/3} = 1$.Thus,the correct option is $C$.

If $x = a \cos^3 \theta$ and $y = b \sin^3 \theta$,then:

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