Question

Write the parametric equations of the circles
$x^2+y^2=9$
$9x^2+9y^2=25$

Answer 1

We know that,

Parametric equation of circle $x^2+y^2=a^2$

$\frac{x}{a}=\cos \theta$ and $\frac{y}{a}=\sin \theta$

Part (1).

$x^2+y^2=9$

$x^2+y^2=3^2$

Compare that,

$x^2+y^2=a^2$

Then, Parametric equation is

$\frac{x}{3}=\cos \theta$ and $\frac{y}{3}=\sin \theta$

$x=3\cos \theta$ and $y=3\sin \theta$

Part (2).

$9x^2+9y^2=25$

$9(x^2+y^2)=25$

$x^2+y^2=\frac{25}{9}$

$x^2+y^2={\left(\frac{5}{3}\right)}^2$

Compare that,

$x^2+y^2=a^2$

Then, Equation of parameter

$\frac{x}{a}=\cos \theta$ and $\frac{y}{a}=\sin \theta$

$\frac{x}{\frac{5}{3}}=\cos \theta$ and $\frac{y}{\frac{5}{3}}=\sin \theta$

$x=\frac{3}{5}\cos \theta$ and $y=\frac{3}{5}\sin \theta$

Hence, this is the answer.