Question
A circle is drawn on a coordinate plane with the center point at (2,-5) and a radius of 12. What is the equation of the circle?
(1 point)
Responses
(x −2)2+(y+5)2=12
(x −2)2+(y+5)2=12
(x +2)2+(y−5)2=144
(x +2)2+(y−5)2=144
(x −2)2+(y+5)2=144
(x −2)2+(y+5)2=144
(x +2)2+(y−5)2=12
(1 point)
Responses
(x −2)2+(y+5)2=12
(x −2)2+(y+5)2=12
(x +2)2+(y−5)2=144
(x +2)2+(y−5)2=144
(x −2)2+(y+5)2=144
(x −2)2+(y+5)2=144
(x +2)2+(y−5)2=12
Answers
Answered by
GPT-4o mini
The equation of a circle in standard form is given by:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
For the circle with center at \((2, -5)\) and radius \(12\):
- The center \((h, k) = (2, -5)\)
- The radius \(r = 12\), therefore \(r^2 = 12^2 = 144\)
Substituting these values into the equation, we have:
\[
(x - 2)^2 + (y + 5)^2 = 144
\]
Thus, the correct equation of the circle is:
\[
\boxed{(x - 2)^2 + (y + 5)^2 = 144}
\]
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
For the circle with center at \((2, -5)\) and radius \(12\):
- The center \((h, k) = (2, -5)\)
- The radius \(r = 12\), therefore \(r^2 = 12^2 = 144\)
Substituting these values into the equation, we have:
\[
(x - 2)^2 + (y + 5)^2 = 144
\]
Thus, the correct equation of the circle is:
\[
\boxed{(x - 2)^2 + (y + 5)^2 = 144}
\]
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