Determine the center and radius of the circle 9x2 54 x 9y2

Determine the center and radius of the circle 9x^2 - 54 x + 9y^2 + 27y + 52 = 0 Center: _____ Radius: _____

Solution

9x^2 -54x +9y^2 +24y +52=0

9(x^2 -6x +9-9)+9(y^2 +8y/3 + 16/9-16/9)=-52

9(x-3)^2 +9(y+4/3)^2=-52 +81 + 16

9(x-3)^2 + 9 (y + 4/3)^2 =45

(x-3)^2 + (y+4/3)^2=(sqrt5)^2

center=(3,-4/3)

Radius=sqrt(5)