Answer
The graph is a circle whose center is at $(1,-\dfrac{1}{2})$ with radius $\dfrac{\sqrt 5}{2}$.
Work Step by Step
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 $r^2=2r \cos \theta -r \sin \theta$
Therefore, our Cartesian equation is $x^2+y^2=2x-y \implies (x-1)^2+(y-\dfrac{1}{2})^2=\dfrac{5}{4}$
This shows that the graph is a circle whose center is at $(1,-\dfrac{1}{2})$ with radius $\dfrac{\sqrt 5}{2}$.
