x^2+y^2−4x+2y−11=0
First, complete squares
x^2-4x +y^2+2y = 11
Determine c1 to complete the first square(x):
c1= (b/2)^2
c1= (-4/2)^2 = (-2)^2 = 4
Then c2 for y
c2= (2/2)^2 = 1^2 = 1
Rewrite:
x^2 -4x +4 +y^2 +2y + 1 = 11 + 4 + 1
Factorize:
(x-2)^2 + (y+1)^2 = 16
Circle equation:
(x-a)^2 + (y-b)^2 = r^2
Where r is the radius
and (a,b) is the center
So, the center of the circle is:
(2,-1) option C
