Question
a circle is centered at -4, 6 and has a radius of 9 units what equation represents the circle
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 your case, the center of the circle is \((-4, 6)\) and the radius is \(9\). Thus, \(h = -4\), \(k = 6\), and \(r = 9\).
Substituting these values into the standard form equation, we have:
\[
(x - (-4))^2 + (y - 6)^2 = 9^2
\]
This simplifies to:
\[
(x + 4)^2 + (y - 6)^2 = 81
\]
So, the equation that represents the circle is:
\[
(x + 4)^2 + (y - 6)^2 = 81
\]
\[
(x - h)^2 + (y - k)^2 = r^2
\]
In your case, the center of the circle is \((-4, 6)\) and the radius is \(9\). Thus, \(h = -4\), \(k = 6\), and \(r = 9\).
Substituting these values into the standard form equation, we have:
\[
(x - (-4))^2 + (y - 6)^2 = 9^2
\]
This simplifies to:
\[
(x + 4)^2 + (y - 6)^2 = 81
\]
So, the equation that represents the circle is:
\[
(x + 4)^2 + (y - 6)^2 = 81
\]