Answer
$x = \frac{y^2}{4}-1$
We can see the graph below:
Work Step by Step
$r = \frac{2}{1-cos~\theta}$
$r-r~cos~\theta = 2$
$\sqrt{x^2+y^2}-x = 2$
$\sqrt{x^2+y^2} = x+2$
$x^2+y^2 = x^2+4x+4$
$y^2 = 4x+4$
$x = \frac{y^2}{4}-1$
We can see the graph below: