Answer
$x^2+(y+2)^2=4$
a circle with center $(0,-2)$, radius $r=2$.
See graph.
Work Step by Step
1. Use the formula $r^2=x^2+y^2, r\ sin\theta=y$, we have $r=-4sin\theta\rightarrow r^2=-4r\ sin\theta \rightarrow x^2+y^2=-4y \rightarrow x^2+(y+2)^2=4$
2. We can identify the above equation as a circle with center $(0,-2)$, radius $r=2$.
3. See graph.
