Answer:
(6, 9 ) and r = 3
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² + y² - 12x - 18y + 108 = 0
Rearrange the x- terms and the y- terms together and subtract 108 from both sides, that is
x² - 12x + y² - 18y = - 108
To obtain standard form use the method of completing the square
add ( half the coefficient of the x and y terms )² to both sides
x² + 2(- 6)x + 36 + y² + 2(- 9)y + 81 = - 108 + 36 + 81
(x - 6)² + (y - 9)² = 9 ← in standard form
with centre = (6, 9 ) and r = = 3