Question
A circle is drawn on a coordinate plane with the center point at (5, 7) and a radius of 3. What is the equation of the circle?(1 point)
Responses
(x − 7)2 + (y−5)2 = 3(x − 7)2 + (y−5)2 = 3
(x − 5)2 + (y−7)2 = 3(x − 5)2 + (y−7)2 = 3
(x − 7)2 + (y−5)2 = 9(x − 7)2 + (y−5)2 = 9
(x − 5)2 + (y−7)2 = 9(x − 5)2 + (y−7)2 = 9
Responses
(x − 7)2 + (y−5)2 = 3(x − 7)2 + (y−5)2 = 3
(x − 5)2 + (y−7)2 = 3(x − 5)2 + (y−7)2 = 3
(x − 7)2 + (y−5)2 = 9(x − 7)2 + (y−5)2 = 9
(x − 5)2 + (y−7)2 = 9(x − 5)2 + (y−7)2 = 9
Answers
GPT-4o mini
The standard form of the 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 \((5, 7)\) and the radius is \(3\).
So, substituting \(h = 5\), \(k = 7\), and \(r = 3\) into the standard form gives:
\[
(x - 5)^2 + (y - 7)^2 = 3^2
\]
\[
(x - 5)^2 + (y - 7)^2 = 9
\]
Thus, the correct equation of the circle is:
\[
\boxed{(x - 5)^2 + (y - 7)^2 = 9}
\]
\[
(x - h)^2 + (y - k)^2 = r^2
\]
In this case, the center of the circle is \((5, 7)\) and the radius is \(3\).
So, substituting \(h = 5\), \(k = 7\), and \(r = 3\) into the standard form gives:
\[
(x - 5)^2 + (y - 7)^2 = 3^2
\]
\[
(x - 5)^2 + (y - 7)^2 = 9
\]
Thus, the correct equation of the circle is:
\[
\boxed{(x - 5)^2 + (y - 7)^2 = 9}
\]