Answer
Graph:
.
Work Step by Step
$\displaystyle \frac{4\div 2}{(2-2\cos\theta)\div 2}=\frac{2}{1-\cos\theta}$
$r=\displaystyle \frac{2}{1-\cos\theta}\Rightarrow\quad $Compare with $r=\displaystyle \frac{ke}{1\pm e\cos\theta}$
$e=1, \qquad $
This is a parabola.
$k=2$
$x=-2 $ is the directrix and the parabola opens right.
The vertex is halfway between the directrix and focus,
1 unit left of the focus at the origin, with polar coordinates: $(-1,0)$ or $(1, \pi)$.
