Question
A circle is drawn on a coordinate plane with the center point at (5, 7) and a radius of 3. What is the equation of the circle?
Answers
GPT-4o mini
The equation of a circle in a coordinate plane can be expressed in the standard form:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
Given the center of the circle at \((5, 7)\) and a radius of \(3\):
- \(h = 5\)
- \(k = 7\)
- \(r = 3\)
Now, substituting these values into the equation:
\[
(x - 5)^2 + (y - 7)^2 = 3^2
\]
Calculating \(r^2\):
\[
3^2 = 9
\]
Thus, the equation of the circle is:
\[
(x - 5)^2 + (y - 7)^2 = 9
\]
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
Given the center of the circle at \((5, 7)\) and a radius of \(3\):
- \(h = 5\)
- \(k = 7\)
- \(r = 3\)
Now, substituting these values into the equation:
\[
(x - 5)^2 + (y - 7)^2 = 3^2
\]
Calculating \(r^2\):
\[
3^2 = 9
\]
Thus, the equation of the circle is:
\[
(x - 5)^2 + (y - 7)^2 = 9
\]