Question 616003
your equation is x^2 + y^2 - 12x + 14y + 17 = 0
put the x's and the y's together to get:
x^2 - 12x + y^2 + 14y + 17 = 0
subtract 17 from both sides of this equation to get:
x^2 - 12x + y^2 + 14y = -17
group your x's and y's together as shown below:
(x^2 - 12x) + (y^2 + 14y) = -17
factor each group by completing the squares on them to get:
(x-6)^2 + (y+7)^2 = -17  + 36 + 49
combine like terms to get:
(x-6)^2 + (y+7)^2 = 68
the center is (6,-7)
the radius is sqrt(68)
here's some references for you.
<a href = "http://www.regentsprep.org/Regents/math/algtrig/ATC1/circlelesson.htm" target = "_blank">http://www.regentsprep.org/Regents/math/algtrig/ATC1/circlelesson.htm</a>
<a href = "http://www.purplemath.com/modules/solvquad3.htm" target = "_blank">http://www.purplemath.com/modules/solvquad3.htm</a>
<a href = "http://www.mathsisfun.com/algebra/circle-equations.html" target = "_blank"http://www.mathsisfun.com/algebra/circle-equations.html></a>