High School

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 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