Answer
The rectangular equation is, ${{\left( x-6 \right)}^{2}}+{{y}^{2}}=36$
Work Step by Step
Using, ${{r}^{2}}={{x}^{2}}+{{y}^{2}}$, we will convert the polar equation to the rectangular equation.
Therefore,
$\begin{align}
& r=12\cos \theta \\
& {{r}^{2}}=12r\cos \theta \\
& {{x}^{2}}+{{y}^{2}}=12r\cos \theta \\
& =12x
\end{align}$
We can further simplify it by completing the square on the x as,
$\begin{align}
& {{x}^{2}}+{{y}^{2}}=12x \\
& {{x}^{2}}+{{y}^{2}}-12x+36=36 \\
& {{\left( x-6 \right)}^{2}}+{{y}^{2}}=36
\end{align}$
