Answer
The graph is a circle whose center is at $(0,-3)$ with radius $3$.
Work Step by Step
Conversion of polar coordinates and Cartesian coordinates are as follows:
a) $r^2=x^2+y^2 \implies r=\sqrt {x^2+y^2}$
b) $\tan \theta =\dfrac{y}{x} \implies \theta =\tan^{-1} (\dfrac{y}{x})$
c) $x=r \cos \theta$
d) $y=r \sin \theta$
Here, we have $r^2\cos^2 \theta +r^2 \sin^2 \theta=-6 r \sin \theta$
Therefore, our Cartesian equation is $x^2+y^2=-6y \implies x^2+(y+3)^2=9$
This shows that the graph is a circle whose center is at $(0,-3)$ with radius $3$.
