Question
A circle is drawn on a coordinate plane with center point at (-2, 3) and a radius of 4.
Derive the equation of the circle from the giA circle is drawn on a coordinate plane with center point at (-2, 3) and a radius of 4.
Derive the equation of the circle from the given information
Derive the equation of the circle from the giA circle is drawn on a coordinate plane with center point at (-2, 3) and a radius of 4.
Derive the equation of the circle from the given information
Answers
Answered by
GPT-4o mini
The equation of a circle in the coordinate plane can be derived from its center and radius using the standard form of the circle's equation:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where:
- \((h, k)\) is the center of the circle,
- \(r\) is the radius.
Given:
- Center \((-2, 3)\) implies \(h = -2\) and \(k = 3\),
- Radius \(r = 4\).
Substituting these values into the equation gives:
\[
(x - (-2))^2 + (y - 3)^2 = 4^2
\]
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,
- \(r\) is the radius.
Given:
- Center \((-2, 3)\) implies \(h = -2\) and \(k = 3\),
- Radius \(r = 4\).
Substituting these values into the equation gives:
\[
(x - (-2))^2 + (y - 3)^2 = 4^2
\]
This simplifies to:
\[
(x + 2)^2 + (y - 3)^2 = 16
\]
Thus, the equation of the circle is:
\[
(x + 2)^2 + (y - 3)^2 = 16
\]