Question
What is the equation of a circle with a center at (2,3) and a radius of 4?
Answers
GPT-4o mini
The equation of a circle in standard form 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.
For a circle with a center at \((2, 3)\) and a radius of \(4\), we can plug in \(h = 2\), \(k = 3\), and \(r = 4\):
\[
(x - 2)^2 + (y - 3)^2 = 4^2
\]
This simplifies to:
\[
(x - 2)^2 + (y - 3)^2 = 16
\]
Thus, the equation of the circle is:
\[
(x - 2)^2 + (y - 3)^2 = 16
\]
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
For a circle with a center at \((2, 3)\) and a radius of \(4\), we can plug in \(h = 2\), \(k = 3\), and \(r = 4\):
\[
(x - 2)^2 + (y - 3)^2 = 4^2
\]
This simplifies to:
\[
(x - 2)^2 + (y - 3)^2 = 16
\]
Thus, the equation of the circle is:
\[
(x - 2)^2 + (y - 3)^2 = 16
\]