Question

Need help with math question

Answer 1

center (1,-3) and radius is 5

Explanation:

We have to use completing the square here:

x^2-2x + y^2+6y =15 (reorder some things and added 15 on both sides)

x^2-2x+(-2/2)^2 + y^2+6y+(6/2)^2 =15+(-2/2)^2+(6/2)^2 (whatever you add on one side you also do to the other side)

x^2-2x+(-1)^2 + y^2+6y+(3)^2=15+1+9

(x-1)^2 + (y+3)^2 =25

Center is (1,-3) and radius is 5

Answer 2

The center is (1,-3) and the radius is r=5 units.

EXPLANATION

The given equation is:

`{x}^(2) + {y}^(2) - 2x + 6y - 15 = 0`

Let rearrange to get:

`{x}^(2) - 2x + {y}^(2) + 6y=15`

We complete the square to get;

`{x}^(2) - 2x + ( { - 1)}^(2) + {y}^(2) + 6y + {3}^(2) = 15+ ( { - 1)}^(2) + {3}^(2)`

`( {x - 1)}^(2) +( {y + 3)}^(2) = 15 + 1+ 9`

`( {x - 1)}^(2) +( {y + 3)}^(2) =25`

`( {x - 1)}^(2) +( {y + 3)}^(2) = {5}^(2)`

Comparing to

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

The center is (1,-3) and the radius is r=5 units.