Question

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

• A. an ellipse
• B. a parabola
• C. a hyperbola
• D. a line pair

Answer 1

Answer: (A)

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