Answer
The graph is a circle with center: $(1,1)$ having radius $\sqrt 2$.
Work Step by Step
The conversion of polar coordinates and Cartesian coordinates are described as follows:
1. $r^2=x^2+y^2$ and $r=\sqrt {x^2+y^2}$
2. $\tan \theta =\dfrac{y}{x} \implies \theta =\tan^{-1} (\dfrac{y}{x})$
3. $x=r \cos \theta$ and 4. $y=r \sin \theta$
Given: $r^2=2r \cos \theta +2r \sin \theta$
Thus, the Cartesian equation is $x^2+y^2=2x+2y $
or, $x^2+y^2=2(x+y) \implies (x-1)^2+(y-1)^2=2$
Hence, this shows that the graph is a circle with center: $(1,1)$ having radius $\sqrt 2$.
