Answer
The polar equation of ${{x}^{2}}+{{y}^{2}}=9$ which express $r$ in terms of $\theta $ is $r=3$.
Work Step by Step
The relation between polar coordinates and rectangular coordinates can be represented as below:
$x=r\cos \theta \ \text{ and }\ y=r\sin \theta $ …… (2)
Substitute the values of $x\ \text{ and }\ y$ from (2) in (1) to get,
$\begin{align}
& {{x}^{2}}+{{y}^{2}}=9 \\
& {{\left( r\cos \theta \right)}^{2}}+{{\left( r\sin \theta \right)}^{2}}=9 \\
& {{r}^{2}}\left( {{\cos }^{2}}\theta +{{\sin }^{2}}\theta \right)=9
\end{align}$
As,
$\left( {{\cos }^{2}}\theta +{{\sin }^{2}}\theta \right)=1$
From here we get,
$\begin{align}
& {{r}^{2}}=9 \\
& r=3
\end{align}$
