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Answer :
To find the radius of circle F, you need to understand the equation of a circle. The general equation of a circle in the coordinate plane 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.
In the given equation of circle F:
[tex]\[
(x + 6)^2 + (y + 8)^2 = 9
\][/tex]
You can compare it with the general equation to identify the circle's characteristics:
- The equation [tex]\((x + 6)^2\)[/tex] can be rewritten as [tex]\((x - (-6))^2\)[/tex], indicating that [tex]\(h = -6\)[/tex].
- The equation [tex]\((y + 8)^2\)[/tex] can be rewritten as [tex]\((y - (-8))^2\)[/tex], indicating that [tex]\(k = -8\)[/tex].
- The term [tex]\((r^2) = 9\)[/tex] tells us the square of the radius.
To find the actual radius, [tex]\(r\)[/tex], you take the square root of [tex]\(9\)[/tex]:
[tex]\[
r = \sqrt{9} = 3
\][/tex]
So, the radius of circle F is [tex]\(3\)[/tex]. The correct answer is:
A. 3
[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.
In the given equation of circle F:
[tex]\[
(x + 6)^2 + (y + 8)^2 = 9
\][/tex]
You can compare it with the general equation to identify the circle's characteristics:
- The equation [tex]\((x + 6)^2\)[/tex] can be rewritten as [tex]\((x - (-6))^2\)[/tex], indicating that [tex]\(h = -6\)[/tex].
- The equation [tex]\((y + 8)^2\)[/tex] can be rewritten as [tex]\((y - (-8))^2\)[/tex], indicating that [tex]\(k = -8\)[/tex].
- The term [tex]\((r^2) = 9\)[/tex] tells us the square of the radius.
To find the actual radius, [tex]\(r\)[/tex], you take the square root of [tex]\(9\)[/tex]:
[tex]\[
r = \sqrt{9} = 3
\][/tex]
So, the radius of circle F is [tex]\(3\)[/tex]. The correct answer is:
A. 3
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