Question

Using the equation x2+y2−8x+2y=8
𝑥
2
+
𝑦
2
−
8
𝑥
+
2
𝑦
=
8
, calculate the center and radius of the circle by completing the square.(1 point)
Responses

center= (2,−8)
(
2
,
−
8
)
, radius=25
center= left parenthesis 2 comma negative 8 right parenthesis , radius=25

center= (8,−2)
(
8
,
−
2
)
, radius=25
center= left parenthesis 8 comma negative 2 right parenthesis , radius=25

center= (4,−1)
(
4
,
−
1
)
, radius=5
center= left parenthesis 4 comma negative 1 right parenthesis , radius=5

center= (−4,1)
(
−
4
,
1
)
, radius=5

Answer 1

Complete the square:

x^2 − 8x + y^2 + 2y = 8
(x − 4)^2 − 16 + (y + 1)^2 − 1 = 8
(x − 4)^2 + (y + 1)^2 = 25

So the center is (4, −1) and the radius is 5.