Answer
The Cartesian form of the provided equation is ${{x}^{2}}+{{y}^{2}}={{6}^{2}}$.
Work Step by Step
The provided equation in polar form is $ r=6$
Therefore, ${{r}^{2}}=36$
As $ x=r\cos \theta \ \text{ and }\ y=r\sin \theta .$ Therefore,
$\begin{align}
& {{x}^{2}}+{{y}^{2}}={{r}^{2}}{{\cos }^{2}}\theta +{{r}^{2}}{{\sin }^{2}}\theta \\
& ={{r}^{2}}\left( {{\cos }^{2}}\theta +{{\sin }^{2}}\theta \right) \\
& ={{r}^{2}}
\end{align}$
Thus, ${{x}^{2}}+{{y}^{2}}={{r}^{2}}$
Also, ${{r}^{2}}=36$
Therefore,
$\begin{align}
& {{x}^{2}}+{{y}^{2}}=36 \\
& {{x}^{2}}+{{y}^{2}}={{6}^{2}} \\
\end{align}$
