Question

Regina is trying to sketch a circle on graph paper with the equation x2+y2−2x+22y+1=0
𝑥
2
+
𝑦
2
−
2
𝑥
+
22
𝑦
+
1
=
0
. Calculate where she would need to graph the center and radius of the circle by completing the square.(1 point)
Responses

center= (−2,22)
(
−
2
,
22
)
, radius=41
center= left parenthesis negative 2 comma 22 right parenthesis , radius=41

center= (1,−11)
(
1
,
−
11
)
, radius=11
center= left parenthesis 1 comma negative 11 right parenthesis , radius=11

center= (−1,11)
(
−
1
,
11
)
, radius=11
center= left parenthesis negative 1 comma 11 right parenthesis , radius=11

center= (−22,2)
(
−
22
,
2
)
, radius=41

Answer 1

Complete the square:

x^2 − 2x = (x − 1)^2 − 1
y^2 + 22y = (y + 11)^2 − 121

So
(x − 1)^2 − 1 + (y + 11)^2 − 121 + 1 = 0
⇒ (x − 1)^2 + (y + 11)^2 = 121

Center = (1, −11), radius = 11.