x2 y2 12x 10y 39 0 is the equation of a circle with center

x^2 + y^2 -12x +10y -39 =0 is the equation of a circle with center (h,k) and radius r for:
h= k= r=

x^2 + y^2 -12x +10y -39 =0

or, x^2 - 12x + y^2 +10y - 39 = 0

or, x^2 - 2*6x + y^2 +2*5y - 39 = 0

or, x^2 - 2*6x + 6^2 + y^2 +2*5y + 5^2 - 39 - 6^2 - 5^2 = 0

or, (x - 6)^2 + (y +5)^2 = 39 + 36 + 25

or, (x - 6)^2 + (y +5)^2 = 100

or, (x - 6)^2 + (y +5)^2 = 10^2

The general formula for circle is , (x - h)^2 + (y - k)^2 = r^2

where, (h,k) is the centre and r is the radius.

In given equation h = 6, k = -5, r = 10