## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

The graph of the equation of a circle ${{x}^{2}}+{{y}^{2}}={{r}^{2}}$ does not include the center as part of the circle.
A circle is defined to be the set of points in a plane that are a fixed distance from the center. Thus, unless $r=0$ and the circle is at one point, the center is not part of the circle. Therefore, the graph of an equation of a circle ${{x}^{2}}+{{y}^{2}}={{r}^{2}}$ does not include the center as part of the circle.