Answer
a. $r=\frac{3}{1+\frac{1}{2}sin\theta}$
b. $e=\frac{1}{2}$, $p=6$, ellipse.
c. See figure.
Work Step by Step
a. Rewrite the equation $r=\frac{6}{2+sin\theta}=\frac{3}{1+\frac{1}{2}sin\theta}$ as the standard form of a conic in polar coordinates.
b. From the above equation, we can determine $e=\frac{1}{2}$ and $ep=3$, which gives $p=6$. With $e\lt1$, the equation can be identified as an ellipse.
c. We can graph the polar equation as shown in the figure.
