Answer
(a ) $e=1$, parabola. (b) See graph.
Work Step by Step
The standard polar forms of conics are $r=\frac{ed}{1\pm e\cdot cos\theta}$ or $r=\frac{ed}{1\pm e\cdot sin\theta}$. And when $e=1$, it represents a parabola, $0\lt e\lt 1$, an ellipse, and $e\gt1$ a hyperbola.
(a) Given the equation $r=\frac{1}{1- cos\theta}$, compare with the standard equation, we can find the eccentricity as $e=1$, and the conic can be identified as a parabola.
(b) See graph
