Answer
The equation represents a circle
$ (x-1)^2+(y^2-1)^2=2^2$
with center $(1,1)$ and radius is $2$
Work Step by Step
$\underline{\textbf{Given equation}}$
$x^2+y^2-2x-2y=2$
$\Rightarrow x^2-2x+y^2-2y=2$
$\Rightarrow (x^2-2x)+(y^2-2y)=2$
$\Rightarrow (x^2-2x+1)+(y^2-2y+1)=2+1+1$
$\Rightarrow (x-1)^2+(y^2-1)^2=2^2$
Which is the standard form for the equation of circle with center $(1,1)$ and radius is $2$
