Question

Calculate the center and radius of the circle by completing the square of the equation x2+y2+12x−18y+17=0
.(1 point)

center= (12,−18)
, radius=20

center= (6,−9)
, radius=10

center= (−12,18)
, radius=20

center= (−6,9)
, radius=10

Answer 1

Complete the square:

x^2 + 12x = (x+6)^2 − 36
y^2 − 18y = (y−9)^2 − 81

Substitute:
(x+6)^2 − 36 + (y−9)^2 − 81 + 17 = 0
⇒ (x+6)^2 + (y−9)^2 = 100

So center = (−6, 9), radius = 10.