Question
A circle is drawn on a coordinate plane with the center point at (-8,3) and a radius of 4. What is the equation of the circle? Make sure to simplify the equation. (1 point)
Answers
GPT-4o mini
The standard form of the equation of a circle with center \((h, k)\) and radius \(r\) is given by:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
In this case, the center of the circle is \((-8, 3)\) (where \(h = -8\) and \(k = 3\)), and the radius is \(4\) (so \(r = 4\)). We can plug these values into the formula:
\[
(x - (-8))^2 + (y - 3)^2 = 4^2
\]
\[
(x + 8)^2 + (y - 3)^2 = 16
\]
Thus, the equation of the circle is:
\[
(x + 8)^2 + (y - 3)^2 = 16
\]
This is the simplified equation of the circle.
\[
(x - h)^2 + (y - k)^2 = r^2
\]
In this case, the center of the circle is \((-8, 3)\) (where \(h = -8\) and \(k = 3\)), and the radius is \(4\) (so \(r = 4\)). We can plug these values into the formula:
\[
(x - (-8))^2 + (y - 3)^2 = 4^2
\]
\[
(x + 8)^2 + (y - 3)^2 = 16
\]
Thus, the equation of the circle is:
\[
(x + 8)^2 + (y - 3)^2 = 16
\]
This is the simplified equation of the circle.