Question
A) 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)
the equation of the circle? Make sure to simplify the equation. (1 point)
Answers
GPT-4o mini
The standard equation of a circle with center at \((h, k)\) and radius \(r\) is given by:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
In this case, the center of the circle is at \((-8, 3)\) (where \(h = -8\) and \(k = 3\)), and the radius is \(4\) (so \(r = 4\)).
Substituting the values into the equation gives us:
\[
(x - (-8))^2 + (y - 3)^2 = 4^2
\]
This simplifies to:
\[
(x + 8)^2 + (y - 3)^2 = 16
\]
Therefore, the equation of the circle is:
\[
(x + 8)^2 + (y - 3)^2 = 16
\]
\[
(x - h)^2 + (y - k)^2 = r^2
\]
In this case, the center of the circle is at \((-8, 3)\) (where \(h = -8\) and \(k = 3\)), and the radius is \(4\) (so \(r = 4\)).
Substituting the values into the equation gives us:
\[
(x - (-8))^2 + (y - 3)^2 = 4^2
\]
This simplifies to:
\[
(x + 8)^2 + (y - 3)^2 = 16
\]
Therefore, the equation of the circle is:
\[
(x + 8)^2 + (y - 3)^2 = 16
\]