# How do you find the center and radius of the circle given #x^2+y^2-18x-18y+53=0#?

##### 1 Answer

Complete the square for the x and y terms to find the center

#### Explanation:

Use a method called "Completing the Square".

1) Group the x terms and y terms. Move the constant term to the right side of the equation by subtracting 53 from both sides.

2) Divide the coefficient of the x term by 2 and then square it.

3) Add the result to both sides.

4) Divide the coefficient of the y term by 2 and then square it.

5) Add the result to both sides.

Factor each set of parentheses. Note that the

Rewrite as the square of a binomial.

Compare this equation to the equation of a circle

where

In this example, the center