The equation of a circle is x^2 + y^2 -4x + 2y -11 =0 . What are the center and the radius of the circle? Show your work.

Answer:The center of the circle;(2, -1)The radius of the circle;r = 4Step-by-step explanation:The first step is to complete the square on both x and y;x^2 + y^2 -4x + 2y - 11 = 0x^2 -4x +y^2 +2y = 11We determine c1 to complete the square on x;c1 = (b/2)^2c1 = (-4/2)^2 = 4We then determine c2 to complete the square on y;c2 = (2/2)^2 = 1The equation of the circle is then re-written as;x^2 -4x + 4 +y^2 +2y + 1 = 11 +4 +1We then factorize the expressions in x and y separately;(x-2)^2 + (y +1)^2 = 16The center of the circle is thus;(2, -1)The radius is the square root of 16;r = 4find the attached.