To find the equation of a circle in the standard [tex]\((x, y)\)[/tex] coordinate plane, we use the general formula for the equation of a circle, which is:
[tex]\[
(x - h)^2 + (y - k)^2 = r^2
\][/tex]
where [tex]\((h, k)\)[/tex] is the center of the circle, and [tex]\(r\)[/tex] is the radius.
Given:
- The center of the circle is [tex]\((8,5)\)[/tex].
- The radius of the circle is 9 units.
We substitute these values into the equation of the circle:
1. Substituting [tex]\(h = 8\)[/tex], [tex]\(k = 5\)[/tex], and [tex]\(r = 9\)[/tex] into the formula, we get:
[tex]\[
(x - 8)^2 + (y - 5)^2 = 9^2
\][/tex]
2. Next, we calculate [tex]\(9^2\)[/tex]:
[tex]\[
9^2 = 81
\][/tex]
3. Therefore, the equation of the circle is:
[tex]\[
(x - 8)^2 + (y - 5)^2 = 81
\][/tex]
From the provided choices, the correct answer is:
F. [tex]\((x - 8)^2 + (y - 5)^2 = 81\)[/tex]
