Question

Write the equation of the circle in standard form.
9x^2 + 9y^2 + 72x − 108y + 368 = 0


Identify its center and radius.
center (x, y) =
radius =

Answer 1

9x^2 + 9y^2 + 72x − 108y + 368 = 0

well put all the x stuff on the left first maybe
9x^2 + 72 x = -9 y^2 +108 y - 368
divide by 9
x^2 + 8 x = -y^2 +12y - 368/9
complete square on left by adding(8/2)^2 = 4^2 = 16 to both sides
x^2 + 8 x + 16 = -y^2 +12 y - 368/9 + 144/9
(x+4)^2 = -y^2 + 12 y - 224/9
now put the y things alone on the left
-y^2 + 12 y = (x+4)^2 + 224/9
do the complete the square thing again
y^2 - 12 y + 36 = -(x+4)^2 - 224/9 + 324/9
(y-6)^2+ (x+4)^2 = r^2 = 100/9 = (10/3)^2