Question

Obtain the parametric equation of the circle $4(x^2+y^2)=9$.

Answer 1

$4(x^2+y^2)=9$
Divide the equation by 4
$x^2+y^2=\frac{9}{4}$

Here, $r^2=\frac{9}{4}⟹r=\frac{3}{2}$

The parametric equations of the circle $x^2+y^2=r^2$ in parameter $\theta$ are $x=r\cos \theta ,y=r\sin \theta$
The parametric equations of the given circle is,
$x=\frac{3}{2}\cos \theta ,y=\frac{3}{2}\sin \theta$ and $0\le \theta \le 2\pi$