## Thomas' Calculus 13th Edition

The graph is a circle with center: $(0,-3)$ having radius $3$.
The conversion of polar coordinates and Cartesian coordinates are described as follows: 1. $r^2=x^2+y^2$ and $r=\sqrt {x^2+y^2}$ 2. $\tan \theta =\dfrac{y}{x} \implies \theta =\tan^{-1} (\dfrac{y}{x})$ 3. $x=r \cos \theta$ and 4. $y=r \sin \theta$ Given: $r^2\cos^2 \theta +r^2 \sin^2 \theta=-6 r \sin \theta$ Thus, the Cartesian equation is $x^2+y^2=-6y$ or, $x^2+(y+3)^2=9$ Hence, this shows that the graph is a circle with center: $(0,-3)$ having radius $3$.