Precalculus (6th Edition) Blitzer

The rectangular equation is, ${{\left( x-6 \right)}^{2}}+{{y}^{2}}=36$
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}