Answer
(a) $x^2+(y-1)^2=1$ (b) circle, center $(0,1)$, radius$=1$. See graph.
Work Step by Step
(a) Use the relations
$r^2=x^2+y^2, r\ sin\theta=y, r\cos\theta=x$,
we have
$r=2sin\theta\Longrightarrow r^2=2r\ sin\theta \Longrightarrow x^2+y^2=2y$ or $x^2+(y-1)^2=1$
(b) We can identify the equation as a circle with center $(0,1)$, radius$=1$ (rectangular system).
See graph.
