## University Calculus: Early Transcendentals (3rd Edition)

The graph is a circle whose center is at $(0,4)$ with radius $4$.
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 $r^2=8r \sin \theta$ Therefore, our Cartesian equation is $x^2+y^2=8y \implies x^2+(y-4)^2=16$ This shows that the graph is a circle whose center is at $(0,4)$ with radius $4$.