Use the following identities:
[tex]r^2 = x^2 + y^2 \\ \\ x = r cos(\alpha) \\ \\ y = r sin(\alpha)[/tex]
First sub for cos:
[tex]r = -2(\frac{x}{r}) \\ \\ r^2 = -2x[/tex]
Now sub for r^2
[tex]x^2 + y^2 = -2x[/tex]
It is now in rectangular form, however, it can be simplified to model a circle equation.
[tex]x^2 + 2x + y^2 = 0 \\ \\ x^2 + 2x+1 + y^2 = 1 \\ \\ (x+1)^2 + y^2 = 1[/tex]
