Answer
(a) $e=\frac{2}{3}$, ellipse. (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) Rewrite the equation as $r=\frac{2/3}{1+\frac{2}{3}sin\theta}$, compare with the standard forms, we can find that $e=\frac{2}{3}$, and we can identify the conic as an ellipse.
(b) See graph
