High School

Circle F is represented by the equation [tex]$(x+6)^2+(y+8)^2=9$[/tex].

What is the length of the radius of circle F?

A. 3
B. 9
C. 10
D. 81

Answer :

To find the length of the radius of the circle represented by the equation [tex]\((x+6)^2 + (y+8)^2 = 9\)[/tex], we first need to recognize the standard form of a circle's equation:

[tex]\[
(x-h)^2 + (y-k)^2 = r^2
\][/tex]

Here, [tex]\((h, k)\)[/tex] represents the center of the circle, and [tex]\(r\)[/tex] is the radius.

In the given equation [tex]\((x+6)^2 + (y+8)^2 = 9\)[/tex]:

- [tex]\((h, k) = (-6, -8)\)[/tex] is the center of the circle.
- The expression equal to 9 represents [tex]\(r^2\)[/tex].

To find the radius [tex]\(r\)[/tex], we take the square root of 9. So:

[tex]\[
r = \sqrt{9} = 3
\][/tex]

Therefore, the length of the radius of circle F is [tex]\(3\)[/tex].

Thus, the correct answer is:
A. 3