Answer
(a) $e=1$, parabola.
(b) See graph.
Work Step by Step
The standard form of a conic polar equation is $r=\frac{ed}{1\pm e\cdot cos\theta}$ or $r=\frac{ed}{1\pm e\cdot sin\theta}$. The graph of the equation will be a parabola if $e=1$, an ellipse if $e\lt1$, and a hyperbola if $e\gt1$
(a) Write the equation given in the Exercise as $r=\frac{2}{1-cos\theta}$, we can identify that $e=1$ by comparing it with a standard equation above. Thus the graph of the equation will be a parabola.
(b) See graph. Vertex $(-1, \pi)$
