How do you find the center and radius of the circle given #x^2+y^2-18x-18y+53=0#?
Complete the square for the x and y terms to find the center
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
In this example, the center