Answer :
To find the length of the radius of circle [tex]\( F \)[/tex], we can analyze the given equation of the circle: [tex]\((x+6)^2+(y+8)^2=9\)[/tex].
The standard form of a circle's equation 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.
Let's break it down:
1. Compare the given equation [tex]\((x+6)^2+(y+8)^2=9\)[/tex] with the standard form [tex]\((x-h)^2 + (y-k)^2 = r^2\)[/tex].
2. In this equation, we can see that:
- [tex]\(h = -6\)[/tex]
- [tex]\(k = -8\)[/tex]
- [tex]\(r^2 = 9\)[/tex]
3. We need to find the radius [tex]\(r\)[/tex], which is the square root of [tex]\(r^2\)[/tex].
4. Calculate the radius:
[tex]\[ r = \sqrt{9} = 3 \][/tex]
Therefore, the length of the radius of circle [tex]\( F \)[/tex] is [tex]\( \boxed{3} \)[/tex].
The standard form of a circle's equation 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.
Let's break it down:
1. Compare the given equation [tex]\((x+6)^2+(y+8)^2=9\)[/tex] with the standard form [tex]\((x-h)^2 + (y-k)^2 = r^2\)[/tex].
2. In this equation, we can see that:
- [tex]\(h = -6\)[/tex]
- [tex]\(k = -8\)[/tex]
- [tex]\(r^2 = 9\)[/tex]
3. We need to find the radius [tex]\(r\)[/tex], which is the square root of [tex]\(r^2\)[/tex].
4. Calculate the radius:
[tex]\[ r = \sqrt{9} = 3 \][/tex]
Therefore, the length of the radius of circle [tex]\( F \)[/tex] is [tex]\( \boxed{3} \)[/tex].
