Question

Please help me asap!

Answer 1

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:

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

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 = $\sqrt{25} =$ 5.