Question
What is the radius of the circle described by the equation (×-6)tiny 2 + (y -4)tiny 2 -64 = 0?
Answers
GPT-4o mini
To find the radius of the circle described by the equation, we start with the given equation:
\[
(x - 6)^2 + (y - 4)^2 - 64 = 0
\]
We can rearrange this equation to isolate the circle on one side:
\[
(x - 6)^2 + (y - 4)^2 = 64
\]
This equation is now in the standard form of a circle, which is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle, and \(r\) is the radius.
From the equation \((x - 6)^2 + (y - 4)^2 = 64\), we can identify:
- \(h = 6\)
- \(k = 4\)
- \(r^2 = 64\)
To find the radius \(r\), we take the square root of \(r^2\):
\[
r = \sqrt{64} = 8
\]
Thus, the radius of the circle is:
\[
\boxed{8}
\]
\[
(x - 6)^2 + (y - 4)^2 - 64 = 0
\]
We can rearrange this equation to isolate the circle on one side:
\[
(x - 6)^2 + (y - 4)^2 = 64
\]
This equation is now in the standard form of a circle, which is:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle, and \(r\) is the radius.
From the equation \((x - 6)^2 + (y - 4)^2 = 64\), we can identify:
- \(h = 6\)
- \(k = 4\)
- \(r^2 = 64\)
To find the radius \(r\), we take the square root of \(r^2\):
\[
r = \sqrt{64} = 8
\]
Thus, the radius of the circle is:
\[
\boxed{8}
\]