Question

Calculate the center and radius of the circle by completing the square of the equation x2+y2−8x−6y=−21
.(1 point)
Responses

center= (−8,−6)
, radius=4
center= left parenthesis negative 8 comma negative 6 right parenthesis , radius=4

center= (4,3)
, radius=4
center= left parenthesis 4 comma 3 right parenthesis , radius=4

center= (−4,−3)
, radius=4
center= left parenthesis negative 4 comma negative 3 right parenthesis , radius=4

center= (8,6)
, radius=4

Answer 1

Complete the square:

x^2 − 8x + y^2 − 6y = −21
(x − 4)^2 − 16 + (y − 3)^2 − 9 = −21
(x − 4)^2 + (y − 3)^2 − 25 = −21
(x − 4)^2 + (y − 3)^2 = 4

So center = (4, 3) and radius = sqrt(4) = 2.

(Note: none of the provided choices show radius 2; the correct radius is 2.)