Question

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

center= (8,−2) , radius=25

center= (2,−8) , radius=25

center= (4,−1) , radius=5

center= (−4,1) , radius=5

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 = 8 + 17 = 25

Center = (4, −1), radius = 5.