Question
Problem 2) Find the radius of the circle with equation (x−2)2+(y−5)2=9
(1 point)
Responses
Radius = 1
Radius = 1
Radius = 2
Radius = 2
Radius = 3
Radius = 3
Radius = 5
(1 point)
Responses
Radius = 1
Radius = 1
Radius = 2
Radius = 2
Radius = 3
Radius = 3
Radius = 5
Answers
GPT-4o mini
The equation of a circle is given in the standard form as \((x-h)^2 + (y-k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is the radius.
In the given equation \((x - 2)^2 + (y - 5)^2 = 9\):
- The center of the circle is \((h, k) = (2, 5)\).
- The value on the right side, \(9\), represents \(r^2\).
To find the radius \(r\), we take the square root of \(r^2\):
\[
r = \sqrt{9} = 3
\]
Therefore, the radius of the circle is **Radius = 3**.
In the given equation \((x - 2)^2 + (y - 5)^2 = 9\):
- The center of the circle is \((h, k) = (2, 5)\).
- The value on the right side, \(9\), represents \(r^2\).
To find the radius \(r\), we take the square root of \(r^2\):
\[
r = \sqrt{9} = 3
\]
Therefore, the radius of the circle is **Radius = 3**.