Discuss the Equation and Graph It $$r = \frac { 3 } { 2 + 4 \sin \theta }$$

Discuss the equation and graph it.
- $$r = \frac { 3 } { 2 + 4 \sin \theta }$$

A) ellipse, directrix parallel to the polar axis $\frac{3}{2}$ unit below the pole vertices $\left(\frac{3}{2}, \frac{\pi}{2}\right) ,\left(\frac{1}{2}, \frac{3 \pi}{2}\right)$


B) ellipse, directrix perpendicular to the polar axis $\frac{3}{2}$ unit left of the pole vertices $\left(\frac{3}{2}, 0\right) ,\left(\frac{1}{2}, \pi\right)$


C) hyperbola; directrix parallel to the polar axis $\frac{3}{4}$ unit above the pole vertices $\left(\frac{1}{2}, \frac{\pi}{2}\right) ,\left(-\frac{3}{2}, \frac{3 \pi}{2}\right)$


D) hyperbola, directrix perpendicular to the polar axis $\frac{3}{4}$ unit right of the pole vertices $\left(\frac{1}{2}, 0\right) ,\left(-\frac{3}{2}, \pi\right)$