Question
What is the radius of the circle?
Question 3 options:
x^2+y^2=1
1
2
3
4
Question 3 options:
x^2+y^2=1
1
2
3
4
Answers
GPT-4o mini
To find the radius of the circle represented by the equation \(x^2 + y^2 = 1\), we need to compare it to the standard form of the equation of a circle, which is given by:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
In the equation \(x^2 + y^2 = 1\), we can see that it matches the standard form with:
- \(h = 0\)
- \(k = 0\)
- \(r^2 = 1\)
To find the radius \(r\), we take the square root of \(r^2\):
\[
r = \sqrt{1} = 1
\]
Thus, the radius of the circle is **1**.
So the correct answer is **1**.
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
In the equation \(x^2 + y^2 = 1\), we can see that it matches the standard form with:
- \(h = 0\)
- \(k = 0\)
- \(r^2 = 1\)
To find the radius \(r\), we take the square root of \(r^2\):
\[
r = \sqrt{1} = 1
\]
Thus, the radius of the circle is **1**.
So the correct answer is **1**.