Chapter 8.2, Problem 66PE

To determine

To calculate: An equation of the form $x^2+y^2+Ax+By+C=0$ that represents the circle that passes through the given points $\left(21,12\right),\left(5,10\right)\text{, and }\left(9,2\right)$ .

To determine

To calculate: The equation of a circle can be written in the form ${(x-h)}^2+{(y-k)}^2=r^2$ , where $\left(h,k\right)$ is the center and $r$ is the radius. Expanding the terms, the equation can also be written in the form $x^2+y^2+Ax+By+C=0$ .

The center and radius of the circle $\left(21,12\right),\left(5,10\right),\left(9,2\right)$ .