# How do you convert r = 1 + 2costheta into rectangular form?

Sep 30, 2016

${\left({x}^{2} + {y}^{2} - 2 x\right)}^{2} = {x}^{2} + {y}^{2}$

#### Explanation:

With the pass equations

$\left\{\begin{matrix}x = r \cos \theta \\ y = r \sin \theta\end{matrix}\right.$ we have

$r = 1 + 2 \frac{x}{r} \to {r}^{2} = r + 2 x$ so

${r}^{2} - 2 x = r \to {\left({r}^{2} - 2 x\right)}^{2} = {r}^{2}$ or

${\left({x}^{2} + {y}^{2} - 2 x\right)}^{2} = {x}^{2} + {y}^{2}$

Attached a plot