(x – h)^2 + (y – k)^2 = r^2 ….(1)

x^2 + y^2 – 6x – 2y – 6 = 0

Add 6 to get the numeric term on the right hand side, and separate the remaining x and y terms:

(x^2 – 6x) + (y^2 – 2y) = 6

Work on the x terms first:

Add to each side of the equation a term equal to the square of half the coefficient of x. That is (-6/2)^2 = -3^2 = 9:

(x^2 – 6x + 9) + (y^2 – 2y) = 6 + 9

Now work on the y terms in the same way. For these, you add (-2/2)^2 = (-1)^2 = 1:

(x^2 – 6x + 9) + (y^2 – 2y + 1) = 6 + 9 + 1

Each of the bracketed expressions on the left can now be factorised as a square:

(x – 3)^2 + (y – 1)^2 = 16 = 4^2.

Comparing this with (1):

h = 3, k = 1, r = 4.

The circle is centred at (3,1) and has radius 4.