Question

Find the center and radius of this circle. x2 + y2 − 40x − 24y + 15 = 0

Answer 1

ANSWER

Center: (20,12)

Radius:23

EXPLANATION

The given circle has equation:

${x}^{2} + {y}^{2} - 40x - 24y + 15 = 0$

We complete the square as follows:

${x}^{2} - 40x + {y}^{2} - 24y = - 15$

${x}^{2} - 40x + {( - 20)}^{2} + {y}^{2} - 24y + {( - 12)}^{2} = - 15+ {( - 20)}^{2}+ {( - 12)}^{2}$

${(x - 20)}^{2} + {(y - 12)}^{2} = - 15+ 400+ 144$

${(x - 20)}^{2} + {(y - 12)}^{2} = 529$

${(x - 20)}^{2} + {(y - 12)}^{2} = {23}^{2}$

Comparing this equation to:

${(x - h)}^{2} + {(y - k)}^{2} = {r}^{2}$

We have

$(h,k)=(20,12)$

representing the center and

$r = 23$

being the radius.