Answer:
The correct answer option is d. (h, k) = (3, -6), r = 5
Step-by-step explanation:
We are given the following equation of a circle:
[tex]x^2+y^2-6x+12y+20=0[/tex]
and we are to find the center and radius of the circle.
Using the completing the square method:
[tex]x^2+y^2-6x+12y=-20[/tex]
Arranging the like terms together to get:
[tex]x^2-6x+y^2+12y=-20[/tex]
Now completing the square by dividing the coefficient of x and y by 2 and adding their squares to each side of the equation:
[tex](x^2-6x+9)+(y^2+12y+36)=-20+9+36[/tex]
Rewriting the equation in the form of perfect squares to get:
[tex](x-3)^2+(y+6)^2=25[/tex]
Comparing it to the standard equation of the circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex] where the center = [tex](h, k)[/tex]
So the coordinates of the center will be (3, -6).
While the radius = [tex]\sqrt{25} =[/tex] 5.
