College Algebra, Chapter 2, 2.2, Section 2.2, Problem 66

Show that the equation $x^2 + y^2 -2x - 2y = 2$ represents a circle. Find the center and radius of the circle.


$
\begin{equation}
\begin{aligned}

x^2 + y^2 - 2x - 2y =& 2
&& \text{Model}
\\
\\
(x^2 - 2x + \underline{}) + (y^2 - 2y + \underline{ }) =& 2
&& \text{Group terms}
\\
\\
(x^2 - 2x + 1) + (y^2 - 2y + 1) =& 2 + 1 + 1
&& \text{Complete the square: add } \left( \frac{-2}{2} \right)^2 = 1, \text{ twice}
\\
\\
(x - 1)^2 + (y - 1)^2 =& 4
&& \text{Perfect Square}

\end{aligned}
\end{equation}
$


Recall that the general equation for the circle with
circle $(h,k)$ and radius $r$ is..

$(x - h)^2 + (y - k)^2 = r^2$

By observation,

The center is at $(1, 1)$ and the radius is 2.