Answer
Parabola
See graph
Work Step by Step
We are given the polar equation:
$r=\dfrac{4}{1-\cos\theta}$
The equation is in the form:
$r=\dfrac{ep}{1-e\cos\theta}$
Determine $e$ using the denominator:
$e=1$
Determine $p$ using the numerator:
$ep=4$
$(1)p=4$
$p=4$
Because $e=1$, the conic is a parabola. Its directrix is perpendicular to the polar axis at a distance of 4 units to the left of the pole. The axis of symmetry is perpendicular to the directrix.
Graph the curve:
