Please show all steps. Thanks!

Find the center of the circle that has the equation

x^2 + 4x + 5 = 12y - y^2

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- May 5th 2009, 11:37 AMcam_ddrtCenter of a circle
Please show all steps. Thanks!

Find the center of the circle that has the equation

x^2 + 4x + 5 = 12y - y^2 - May 5th 2009, 12:47 PMSoroban
Hello, cam_ddrt!

You've never done one of these before?

And no one has ever shown you how?

Quote:

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: .$\displaystyle (-2,\:6)$