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