# How do you convert the rectangular equation x^2 + y^2 = 6x to polar form?

Dec 6, 2015

$r = 6 \cos \left(\theta\right)$

#### Explanation:

${x}^{2} + {y}^{2} = {r}^{2} \textcolor{w h i t e}{\text{XXXXXXXX}}$[1]

$\frac{x}{r} = \cos \left(\theta\right)$

$\rightarrow x = r \cdot \cos \left(\theta\right)$

$\rightarrow 6 x = 6 r \cdot \cos \left(\theta\right) \textcolor{w h i t e}{\text{XXXX}}$[2]

Combining [1] and [2]
${x}^{2} + {y}^{2} = 6 x$

$\rightarrow {r}^{2} = 6 r \cdot \cos \left(\theta\right)$

$\rightarrow r = 6 \cos \left(\theta\right)$