Question

write the standard form of the equation of the circle with the given center and radius. center (2, - 6), r = 8
type the standard form of the equation of the circle.
(simplify your answer.)

Explanation:

Step1: Recall circle - equation formula

The standard - form equation of a circle is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center of the circle and $r$ is the radius.

Step2: Identify values of $h$, $k$, and $r$

Given that the center is $(2,-6)$ and $r = 8$, so $h = 2$, $k=-6$, and $r = 8$.

Step3: Substitute values into the formula

Substitute $h = 2$, $k=-6$, and $r = 8$ into $(x - h)^2+(y - k)^2=r^2$, we get $(x - 2)^2+(y+6)^2=64$.

Answer:

$(x - 2)^2+(y + 6)^2=64$