Please show all steps. Thanks!
Find the center of the circle that has the equation
x^2 + 4x + 5 = 12y - y^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: .$\displaystyle
x^2 + 4x + 5 \:= \:12y - y^2$
Rearrange the terms: .$\displaystyle x^2 + 4x + y^2 - 12y \:=\:-5$
Complete the square: .$\displaystyle x^2 + 4x + {\color{blue}4} + y^2 - 12y + {\color{red}36} \:=\:-5 + {\color{blue}4} + {\color{red}36} $
And we have: .$\displaystyle (x+2)^2 + (y-6)^2 \:=\:35$
The center is: .$\displaystyle (-2,\:6)$