### Home > PC > Chapter 7 > Lesson 7.2.4 > Problem7-81

7-81.

Complete the square (if necessary) to find the center and radius of the circle. Then sketch the graph.

1. $x^{2} + y^{2} − 10x + 8y + 5 = 0$

Regroup with $x'\text{s}$ and y's together and the constant on the other side.

$\left(x^{2} − 10x \:+\: ?\right) + \left(y^{2} + 8y \:+\: ?\right) = − 5$

Complete the square finding the ?'s and adding the same amount on both sides.

$\left(x^{2} − 10x + 25\right) + \left(y^{2} + 8y + 16\right) = − 5 + 25 + 16$

Simplify and graph.

$\left(x − 5\right)^{2} + \left(y + 4\right)^{2} = 36$

1. $x^{2} + y^{2} − 8x + 6y − 56 ≤ 0$

Follow the same thinking process as part (a).