# How do you convert the rectangular equation (x - 2)^2 + y^2 = 9# into polar form?

${r}^{2} = 5 + 4 r \cos \theta$

#### Explanation:

${r}^{2} {\cos}^{2} \theta - 4 r \cos \theta + 4 + {r}^{2} {\sin}^{2} \theta = 9$

${r}^{2} {\cos}^{2} \theta + {r}^{2} {\sin}^{2} \theta - 4 r \cos \theta + 4 = 9$

${r}^{2} \left({\cos}^{2} \theta + {\sin}^{2} \theta\right) - 4 r \cos \theta + 4 = 9$

but $\left({\cos}^{2} \theta + {\sin}^{2} \theta\right) = 1$

therefore

${r}^{2} \cdot 1 - 4 r \cos \theta + 4 = 9$

${r}^{2} = 5 + 4 r \cos \theta$

Have a nice day !!! from the Philippines...