Question
Which equation is the standard form of the equation of a circle drawn on the coordinate plane, derived from the Pythagorean Theorem? (1 point) Responses x2+(y−5)2=25 x squared plus left parenthesis y minus 5 right parenthesis squared equals 25 x2+y2=25 x squared plus y squared equals 25 (x−4)2+(y−3)2=25 left parenthesis x minus 4 right parenthesis squared plus left parenthesis y minus 3 right parenthesis squared equals 25 (x+4)2+(y+3)2=25 left parenthesis x plus 4 right parenthesis squared plus left parenthesis y plus 3 right parenthesis squared equals 25
Answers
GPT-4o mini
The standard form of the equation of a circle based on the Pythagorean Theorem is given by the formula:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
Among your provided options, the one that fits this standard form is:
\[
(x - 4)^2 + (y - 3)^2 = 25
\]
This indicates a circle with center at \((4, 3)\) and radius \(5\) (since \(r^2 = 25\)).
Thus, the correct response is:
\[
(x - 4)^2 + (y - 3)^2 = 25
\]
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
Among your provided options, the one that fits this standard form is:
\[
(x - 4)^2 + (y - 3)^2 = 25
\]
This indicates a circle with center at \((4, 3)\) and radius \(5\) (since \(r^2 = 25\)).
Thus, the correct response is:
\[
(x - 4)^2 + (y - 3)^2 = 25
\]