Question 781417
You want the equation in a form, {{{(x-h)^2+(y-k)^2=r^2}}} in which the center is (h,k) and radius is r.  This is a Complete-the-Square problem.


{{{x^2+y^2+4x-8y+13=0}}}
{{{x^2+4x+y^2-8y+13=0}}}

The  terms with x need {{{(4/2)^2=4}}} and the terms with y need {{{(-8/2)^2=16}}}


{{{(x^2+4x+4)+(y^2-8y+16)+13=4+16}}}
{{{(x+2)^2+(y-4)^2+13=20
{{{highlight((x+2)^2+(y-4)^2=7)}}}
(x+2)^2+(y-4)^2=7


Center: (-2,4)
Radius: sqrt(7)