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