x^2 + y^2 - 4x + 2y - 11 = 0
Rearrange as
x^2- 4x + y^2 + 2y = 11
We need to complete the square on x an y
I'm assuming that you know how to do this...if, not...here's a good resource :
http://www.purplemath.com/modules/sqrcircle.htm
x^2 - 4x + 4 + y^2 + 2y + 1 = 11 + 4 + 1 factor and simplify
(x - 2)^2 + (y + 1)^2 = 16
In the form ( x - h)^2 + (y - k)^2 = r^2
The center is (h, k) and the radius = r ......so....we can write
( x - 2)^2 + ( y - (-1) )^2 = 4^2
The center is (2, - 1) and the radius is 4