Answer
It is a limaçon with inner loop.
Work Step by Step
Main points:
$θ=0$:
$r=3$
This point passes through the x-axis at $x=3$
$r$ increases from $0\ltθ\lt\frac{\pi}{2}$...
$θ=\frac{\pi}{2}$:
$r=9$
This point passes through the y-axis at $y=9$
$r$ decreases from $\frac{\pi}{2}\ltθ\lt\pi$...
$θ=\pi$:
$r=3$
This point passes through the x-axis at $x=-3$
$r$ decreases from $\pi\ltθ\lt\frac{7\pi}{6}$...
$θ=\frac{7\pi}{6}$:
$r=0$
This point passes at the origin.
$r$ increases from $\frac{7\pi}{6}\ltθ\lt\frac{3\pi}{2}$...
$θ=\frac{3\pi}{2}$:
$r=-3$
This point passes through the y-axis at $y=3$
$r$ decreases from $\frac{3\pi}{2}\ltθ\lt\frac{11\pi}{6}$...
$θ=\frac{11\pi}{6}$:
$r=0$
This point passes at the origin.
$r$ increases from $\frac{11\pi}{6}\ltθ\lt2\pi$...
$θ=2\pi$:
$r=3$
This point passes through the x-axis at $x=3$
