Answer :
To find the length of the radius of circle [tex]\(F\)[/tex], let's start by analyzing the given equation of the circle:
[tex]\[
(x+6)^2 + (y+8)^2 = 9
\][/tex]
This equation is in the standard form of a circle, which is:
[tex]\[
(x - h)^2 + (y - k)^2 = r^2
\][/tex]
In this form, [tex]\((h, k)\)[/tex] represents the center of the circle, and [tex]\(r\)[/tex] is the radius.
Comparing the given equation to the standard form:
- The equation [tex]\((x+6)^2\)[/tex] can be rewritten as [tex]\((x - (-6))^2\)[/tex], and [tex]\((y+8)^2\)[/tex] as [tex]\((y - (-8))^2\)[/tex]. This tells us that the center of the circle is [tex]\((-6, -8)\)[/tex].
- The number on the right side of the equation is 9, which is equal to [tex]\(r^2\)[/tex], the square of the radius.
To find the radius [tex]\(r\)[/tex], we need to take the square root of 9:
[tex]\[
r = \sqrt{9} = 3
\][/tex]
Thus, the length of the radius of circle [tex]\(F\)[/tex] is 3.
The correct answer is:
A. 3
[tex]\[
(x+6)^2 + (y+8)^2 = 9
\][/tex]
This equation is in the standard form of a circle, which is:
[tex]\[
(x - h)^2 + (y - k)^2 = r^2
\][/tex]
In this form, [tex]\((h, k)\)[/tex] represents the center of the circle, and [tex]\(r\)[/tex] is the radius.
Comparing the given equation to the standard form:
- The equation [tex]\((x+6)^2\)[/tex] can be rewritten as [tex]\((x - (-6))^2\)[/tex], and [tex]\((y+8)^2\)[/tex] as [tex]\((y - (-8))^2\)[/tex]. This tells us that the center of the circle is [tex]\((-6, -8)\)[/tex].
- The number on the right side of the equation is 9, which is equal to [tex]\(r^2\)[/tex], the square of the radius.
To find the radius [tex]\(r\)[/tex], we need to take the square root of 9:
[tex]\[
r = \sqrt{9} = 3
\][/tex]
Thus, the length of the radius of circle [tex]\(F\)[/tex] is 3.
The correct answer is:
A. 3
