# How do you find the center and radius of the circle x^2 + y^2 − 10x + 8y + 32 = 0?

Oct 16, 2016

The center is $\left(5 , - 4\right)$ and the radius is 3

#### Explanation:

${x}^{2} - 10 x + {y}^{2} + 8 y + 32 = 0$
Completing the squares
${x}^{2} - 10 x + 25 + {y}^{2} + 8 y + 16 = - 32 + 25 + 16$
${\left(x - 5\right)}^{2} + {\left(y + 4\right)}^{2} = 9 = {3}^{2}$
So the center is $\left(5 , - 4\right)$ and the radius is 3
See the graph below
graph{x^2-10x+y^2+8y+32=0 [-20, 20, -10, 10]}