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  4. The graph of x=3 cos ( sin -1 (y/2)) represents

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Q. The graph of $x=3 \cos \left(\sin ^{-1} \frac{y}{2}\right)$ represents

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Solution:

$\frac{x}{3}=\cos \theta$ where $\sin \theta=\frac{y}{2}$
$\frac{x^2}{9}=\cos ^2 \theta=1-\frac{y^2}{4} \Rightarrow \frac{x^2}{9}+\frac{y^2}{4}=1$