Question
A circle has a center at (3,−5) and a radius of 8 units. What is the domain of the circle? (1 point)
Answers
GPT-4o mini
To find the domain of a circle, we need to determine the horizontal extent (x-values) that the circle covers. A circle centered at \((h, k)\) with a radius \(r\) can be described by the equation:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
In this case, the center of the circle is \((3, -5)\) and the radius is \(8\).
The domain of the circle is determined by the center's x-coordinate and the radius. The x-coordinate of the center is \(3\), and the radius \(8\) extends \(8\) units in both directions from the center.
Thus, the leftmost point is:
\[
3 - 8 = -5
\]
And the rightmost point is:
\[
3 + 8 = 11
\]
Therefore, the domain of the circle in interval notation is:
\[
[-5, 11]
\]
So the domain of the circle is \([-5, 11]\).
\[
(x - h)^2 + (y - k)^2 = r^2
\]
In this case, the center of the circle is \((3, -5)\) and the radius is \(8\).
The domain of the circle is determined by the center's x-coordinate and the radius. The x-coordinate of the center is \(3\), and the radius \(8\) extends \(8\) units in both directions from the center.
Thus, the leftmost point is:
\[
3 - 8 = -5
\]
And the rightmost point is:
\[
3 + 8 = 11
\]
Therefore, the domain of the circle in interval notation is:
\[
[-5, 11]
\]
So the domain of the circle is \([-5, 11]\).