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Question: If \(x = a\cos^{3}\theta,y = b\sin^{3}\theta,\) then...

If x=acos⁡3θ,y=bsin⁡3θ,x = a\cos^{3}\theta,y = b\sin^{3}\theta, then

A

(ax)2/3+(by)2/3=1\left( \frac{a}{x} \right)^{2/3} + \left( \frac{b}{y} \right)^{2/3} = 1

B

(bx)2/3+(ay)2/3=1\left( \frac{b}{x} \right)^{2/3} + \left( \frac{a}{y} \right)^{2/3} = 1

C

(xa)2/3+(yb)2/3=1\left( \frac{x}{a} \right)^{2/3} + \left( \frac{y}{b} \right)^{2/3} = 1

D

(xb)2/3+(ya)2/3=1\left( \frac{x}{b} \right)^{2/3} + \left( \frac{y}{a} \right)^{2/3} = 1

Answer

(xa)2/3+(yb)2/3=1\left( \frac{x}{a} \right)^{2/3} + \left( \frac{y}{b} \right)^{2/3} = 1

Explanation

Solution

(xa)1/3=cos⁡θ,(yb)1/3=sin⁡θ\left( \frac{x}{a} \right)^{1/3} = \cos\theta,\left( \frac{y}{b} \right)^{1/3} = \sin\theta

Now square and add.