Question

Please help me asap!

Answer 1

The correct answer option is d. (h, k) = (3, -6), r = 5

Explanation:

We are given the following equation of a circle:

`x^2+y^2-6x+12y+20=0`

and we are to find the center and radius of the circle.

Using the completing the square method:

`x^2+y^2-6x+12y=-20`

Arranging the like terms together to get:

`x^2-6x+y^2+12y=-20`

Now completing the square by dividing the coefficient of x and y by 2 and adding their squares to each side of the equation:

`(x^2-6x+9)+(y^2+12y+36)=-20+9+36`

Rewriting the equation in the form of perfect squares to get:

`(x-3)^2+(y+6)^2=25`

Comparing it to the standard equation of the circle:

`(x-h)^2+(y-k)^2=r^2` where the center =
`(h, k)`

So the coordinates of the center will be (3, -6).

While the radius =
`√(25) =` 5.