Answer
The required polar equation is $r=10$.
Work Step by Step
To find the polar equation substitute $x=r\cos \theta \ \text{ and }\ y=r\sin \theta $ in the provided equation, where r is the distance of that point from the origin and $\theta $ is the respective angle.
So,
$\begin{align}
& {{x}^{2}}+{{y}^{2}}=100 \\
& {{\left( r\cos \theta \right)}^{2}}+{{\left( r\sin \theta \right)}^{2}}=100 \\
& {{r}^{2}}\left( {{\cos }^{2}}\theta +{{\sin }^{2}}\theta \right)=100
\end{align}$
Since, ${{\cos }^{2}}\theta +{{\sin }^{2}}\theta =1$ so,
$\begin{align}
& {{r}^{2}}\left( {{\cos }^{2}}\theta +{{\sin }^{2}}\theta \right)=100 \\
& {{r}^{2}}=100 \\
& r=10
\end{align}$
Therefore, the polar equation of the equation ${{x}^{2}}+{{y}^{2}}=100$ is $r=10$.
