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Select the correct answer.

Circle F is represented by the equation [tex]\((x+6)^2+(y+8)^2=9\)[/tex]. What is the length of the radius of circle F?

A. 3
B. 9
C. 10
D. 81

Answer :

To find the length of the radius of Circle F, we first need to understand the standard form equation of a circle, which is:

[tex]\[
(x-h)^2 + (y-k)^2 = r^2
\][/tex]

In this equation:
- [tex]\((h, k)\)[/tex] is the center of the circle.
- [tex]\(r\)[/tex] is the radius of the circle.

For Circle F, the equation is given as:

[tex]\[
(x+6)^2 + (y+8)^2 = 9
\][/tex]

Let's compare this to the standard form. We can see:
- The center of the circle [tex]\((h, k)\)[/tex] is [tex]\((-6, -8)\)[/tex].
- The right side of the equation is [tex]\(r^2\)[/tex], which is 9.

Now, to find [tex]\(r\)[/tex], the radius, we need to take the square root of [tex]\(r^2\)[/tex]:

[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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