x^2+y^2+16x−24y+159=0 .

x^2+y^2+16x−24y+159=0   

x^2 + 16x  + y^2 - 24y   =  -159        complete the square on x and y

x^2 + 16x  +  64  + y^2 - 24y  + 144   =   -159 + 64 + 144        factor

(x  +  8)^2   + (y - 12)^2   =  49

The center is  ( -8, 12 )