ANSWER
Center: (20,12)
Radius:23
EXPLANATION
The given circle has equation:
[tex]{x}^{2} + {y}^{2} - 40x - 24y + 15 = 0[/tex]
We complete the square as follows:
[tex]{x}^{2} - 40x + {y}^{2} - 24y = - 15[/tex]
[tex]{x}^{2} - 40x + {( - 20)}^{2} + {y}^{2} - 24y + {( - 12)}^{2} = - 15+ {( - 20)}^{2}+ {( - 12)}^{2}[/tex]
[tex] {(x - 20)}^{2} + {(y - 12)}^{2} = - 15+ 400+ 144[/tex]
[tex] {(x - 20)}^{2} + {(y - 12)}^{2} = 529[/tex]
[tex]{(x - 20)}^{2} + {(y - 12)}^{2} = {23}^{2} [/tex]
Comparing this equation to:
[tex]{(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]
We have
[tex](h,k)=(20,12)[/tex]
representing the center and
[tex]r = 23[/tex]
being the radius.
