Answer
Center: (1,-12)
Radius: 5
Work
[tex]x^{2}[/tex]+[tex]y^{2}[/tex]-2x+24y+120=0 (Subtract 120 on both sides and rearrange)
[tex]x^{2}[/tex]-2x+[tex]y^{2}[/tex]+24y=-120 (Then divide 2 by 2 and square it. Do the same for 24.)
[tex]x^{2}[/tex]-2x+1+[tex]y^{2}[/tex]+24y+144=-120+1+144 (You have to add the same numbers on both sides)
[tex](x-1)^{2} +(y+12)^2=25[/tex] (Simplify)
So you would put (1,-12); r=5
