Answer
$$ x^2+y^2-2y=0$$
Work Step by Step
Recall that $x^2+y^2=r^2$ and $r\sin \theta=y$:
\begin{align*}
r&=2\sin \theta \\
r^2 &=2r\sin \theta \\
x^2+y^2&=2y
\end{align*}
then
$$ x^2+y^2-2y=0$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.3 Polar Coordinates - Exercises - Page 617: 13
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