Question

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

center= (−4,1)
, radius=5

center= (4,−1)
, radius=5

center= (8,−2)
, radius=25

center= (2,−8)
, radius=25

Answer 1

Complete the square:

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

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

Center = (4, −1), radius = 5.