Question
Formula for a circle
Answers
GPT-4o mini
The formula for a circle depends on its position in the coordinate system and can be expressed in different forms. The most common form is the standard 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,
- \(r\) is the radius of the circle,
- \((x, y)\) are the coordinates of any point on the circle.
If the center of the circle is at the origin (0, 0), the equation simplifies to:
\[
x^2 + y^2 = r^2
\]
This represents all the points that are a distance \(r\) from the origin.
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where:
- \((h, k)\) is the center of the circle,
- \(r\) is the radius of the circle,
- \((x, y)\) are the coordinates of any point on the circle.
If the center of the circle is at the origin (0, 0), the equation simplifies to:
\[
x^2 + y^2 = r^2
\]
This represents all the points that are a distance \(r\) from the origin.