Question
Use the image to answer the question.
A circle is plotted on a coordinate plane.
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
(x−2)2+(y+2)2=16
left parenthesis x minus 2 right parenthesis squared plus left parenthesis y plus 2 right parenthesis squared equals 16
(x−2)2+(y−2)2=4
left parenthesis x minus 2 right parenthesis squared plus left parenthesis y minus 2 right parenthesis squared equals 4
(x+2)2+(y−6)2=4
left parenthesis x plus 2 right parenthesis squared plus left parenthesis y minus 6 right parenthesis squared equals 4
(x−6)2+(y−2)2=16
A circle is plotted on a coordinate plane.
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
(x−2)2+(y+2)2=16
left parenthesis x minus 2 right parenthesis squared plus left parenthesis y plus 2 right parenthesis squared equals 16
(x−2)2+(y−2)2=4
left parenthesis x minus 2 right parenthesis squared plus left parenthesis y minus 2 right parenthesis squared equals 4
(x+2)2+(y−6)2=4
left parenthesis x plus 2 right parenthesis squared plus left parenthesis y minus 6 right parenthesis squared equals 4
(x−6)2+(y−2)2=16
Answers
GPT-4o mini
To determine the standard form of the equation of a circle, we use the formula:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
Without the image to refer to, here’s how to analyze each option based on the standard form:
1. \((x−2)^2+(y+2)^2=16\) - This implies the center is at (2, -2) and radius is 4 (since \(r^2 = 16\)).
2. \((x−2)^2+(y−2)^2=4\) - This suggests the center is at (2, 2) and radius is 2 (since \(r^2 = 4\)).
3. \((x+2)^2+(y−6)^2=4\) - Here, the center is at (-2, 6) and radius is 2.
4. \((x−6)^2+(y−2)^2=16\) - This indicates the center is at (6, 2) and radius is 4.
To select the correct equation, you would need to identify the center and radius of the circle displayed in the image. Given the information above, if the center and radius of the circle corresponded to one of these equations, that would be your answer.
Please refer to the provided options and identify the center and radius from the image to find the correct equation.
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
Without the image to refer to, here’s how to analyze each option based on the standard form:
1. \((x−2)^2+(y+2)^2=16\) - This implies the center is at (2, -2) and radius is 4 (since \(r^2 = 16\)).
2. \((x−2)^2+(y−2)^2=4\) - This suggests the center is at (2, 2) and radius is 2 (since \(r^2 = 4\)).
3. \((x+2)^2+(y−6)^2=4\) - Here, the center is at (-2, 6) and radius is 2.
4. \((x−6)^2+(y−2)^2=16\) - This indicates the center is at (6, 2) and radius is 4.
To select the correct equation, you would need to identify the center and radius of the circle displayed in the image. Given the information above, if the center and radius of the circle corresponded to one of these equations, that would be your answer.
Please refer to the provided options and identify the center and radius from the image to find the correct equation.