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

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

Thus center = (−6, 9) and radius = 10.