Answer
Graph:
Work Step by Step
Sine in the denominator: so the main axis is vertical.
We want $1\pm...$ in the denominator,
$\displaystyle \frac{12\div 3}{(3+3\sin\theta)\div 3}$=$\displaystyle \frac{4}{1+(1)\sin\theta}$
Compare with $r=\displaystyle \frac{ke}{1\pm e\sin\theta}$
$e=1$
Thus this is a parabola.
$k=4$
$y=4$ is the directrix, so the parabola opens down.
The vertex is halfway between the directrix and focus,
2 units above the focus at the origin, on the y-axis $(\theta=\pi/2)$ with polar coordinates: $(2,\pi/2).$
