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
[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
