Question 126884
Start with the general formula for a circle
{{{(x - h)^2 + (y - k)^2 = r^2}}}
Somehow you have to get your equation into that form
{{{x^2 + y^2 - 12x + 6y + 35 = 0}}}
Group the x terms together and the y terms together
and subtract {{{35}}} from both sides
{{{x^2 - 12x + y^2 + 6y = -35}}}
Now do the operation called completing the square
on the x terms and the y terms
You do that by taking 1/2 of the coefficient of 
x (or y), squaring it, then add it to both sides
{{{x^2 - 12x + (12/2)^2 + y^2 + 6y + (6/2)^2 = -35 + (12/2)^2 + (6/2)^2}}}
Notice that this is the exact same equation
I started with because I added the same thing to BOTH sides
{{{x^2 - 12x + 36 + y^2 + 6y + 9 = -35 + 36 + 9}}}
Now you can get this into the form
{{{(x - h)^2 + (y - k)^2 = r^2}}}
{{{(x - 6)^2 + (y + 3)^2 = 10}}}
If you just match up the terms, you see that
{{{h = 6}}}
{{{k = -3}}}
{{{r^2 = 10}}}
{{{r = sqrt(10)}}}
So, the center is at (6,-3) and the radius is {{{sqrt(10)}}}