Answer
See image:
Work Step by Step
$\displaystyle \frac{4\div 2}{(2-2\cos\theta)\div 2}=\frac{2}{1-\cos\theta}$
$r=\displaystyle \frac{2}{1-\cos\theta}$
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, so the parabola opens right.
The vertex is halfway between the directrix and the focus,
1 unit left of the focus at the origin.
The polar coordinates are: $(-1,0)$ or $(1, \pi)$
