Question

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

Answer 1

Center: (20,12)

Radius:23

Step-by-step 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.