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Answer :
To find the length of the radius of the circle, let's start by understanding the given equation of the circle: [tex]\((x + 6)^2 + (y + 8)^2 = 9\)[/tex].
The standard form of a circle 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 compare the given equation with the standard form:
1. Identify the center [tex]\((h, k)\)[/tex]:
The equation [tex]\((x + 6)^2 + (y + 8)^2 = 9\)[/tex] can be rewritten as [tex]\((x - (-6))^2 + (y - (-8))^2 = 9\)[/tex].
This means the center of the circle is [tex]\((-6, -8)\)[/tex].
2. Identify [tex]\(r^2\)[/tex]:
The right side of the equation is 9, which represents [tex]\(r^2\)[/tex].
3. Find the radius [tex]\(r\)[/tex]:
To find the radius, we take the square root of [tex]\(r^2\)[/tex].
So, [tex]\(r = \sqrt{9} = 3\)[/tex].
Therefore, the length of the radius of circle F is [tex]\(3\)[/tex].
The correct answer is A. 3.
The standard form of a circle 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 compare the given equation with the standard form:
1. Identify the center [tex]\((h, k)\)[/tex]:
The equation [tex]\((x + 6)^2 + (y + 8)^2 = 9\)[/tex] can be rewritten as [tex]\((x - (-6))^2 + (y - (-8))^2 = 9\)[/tex].
This means the center of the circle is [tex]\((-6, -8)\)[/tex].
2. Identify [tex]\(r^2\)[/tex]:
The right side of the equation is 9, which represents [tex]\(r^2\)[/tex].
3. Find the radius [tex]\(r\)[/tex]:
To find the radius, we take the square root of [tex]\(r^2\)[/tex].
So, [tex]\(r = \sqrt{9} = 3\)[/tex].
Therefore, the length of the radius of circle F is [tex]\(3\)[/tex].
The correct answer is A. 3.
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