The standard form for a circle is:
(x-h)2 + (y-k)2 = r2
Where (h,k) is the center of the circle and r is its radius. The equation in the problem is:
x2 - 10x + y2 + 8y = 11
We need to put this equation into standard form by "completing the square" for the x terms and the y terms. The parts that we add to complete the square are shown in orange. We have add the same stuff to the other side of the equation to keep it equal.
[x2 - 10x + (-10/2)2] + [y2 + 8y + (8/2)2] = 11 + (-10/2)2 + (8/2)2
(x2-10x+25) + (y2+8y+16) = 11 + 25 + 16
(x-5)2 + (y+4)2 = 52
r2 = 52
r = √52 = √(4*13) = 2√13 ≅ 7.2
