Question

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

center= (−22,2)
, radius=41

center= (−2,22)
, radius=41

center= (−1,11)
, radius=11

center= (1,−11)
, radius=11

Answer 1

x^2 + y^2 − 2x + 22y + 1 = 0
Rewrite by completing squares:
(x^2 − 2x + 1) + (y^2 + 22y + 121) + 1 − 1 − 121 = 0
=> (x − 1)^2 + (y + 11)^2 − 121 = 0
=> (x − 1)^2 + (y + 11)^2 = 121

So center = (1, −11) and radius = sqrt(121) = 11.