Question

Calculate the center and radius of the circle by completing the square of the equation x2+y2+12x−18y+17=0
𝑥
2
+
𝑦
2
+
12
𝑥
−
18
𝑦
+
17
=
0
.(1 point)
Responses

center= (12,−18)
(
12
,
−
18
)
, radius=20
center= left parenthesis 12 comma negative 18 right parenthesis , radius=20

center= (−6,9)
(
−
6
,
9
)
, radius=10
center= left parenthesis negative 6 comma 9 right parenthesis , radius=10

center= (6,−9)
(
6
,
−
9
)
, radius=10
center= left parenthesis 6 comma negative 9 right parenthesis , radius=10

center= (−12,18)
(
−
12
,
18
)
, radius=20

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

Center = (−6, 9), radius = 10.