# Thread: Center of a circle

1. ## Center of a circle

Find the center of the circle that has the equation
x^2 + 4x + 5 = 12y - y^2

2. Hello, cam_ddrt!

You've never done one of these before?
And no one has ever shown you how?

Find the center of the circle: . $
x^2 + 4x + 5 \:= \:12y - y^2$

Rearrange the terms: . $x^2 + 4x + y^2 - 12y \:=\:-5$

Complete the square: . $x^2 + 4x + {\color{blue}4} + y^2 - 12y + {\color{red}36} \:=\:-5 + {\color{blue}4} + {\color{red}36}$

And we have: . $(x+2)^2 + (y-6)^2 \:=\:35$

The center is: . $(-2,\:6)$