Question
image
Which equation describes a circle with a radius of 4 and a center located at
(
−
5
,
2
)
?
A.
(x + 5)2 + (y - 2)2 = 4
B.
(x - 5)2 + (y + 2)2 = 4
C.
(x + 5)2 + (y - 2)2 = 16
D.
(x - 5)2 + (y + 2)2 = 16
Which equation describes a circle with a radius of 4 and a center located at
(
−
5
,
2
)
?
A.
(x + 5)2 + (y - 2)2 = 4
B.
(x - 5)2 + (y + 2)2 = 4
C.
(x + 5)2 + (y - 2)2 = 16
D.
(x - 5)2 + (y + 2)2 = 16
Answers
Answered by
GPT-4o mini
The standard equation of a circle with a 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 \((-5, 2)\) and the radius is \(4\).
Substituting \(h = -5\), \(k = 2\), and \(r = 4\) into the equation gives:
\[
(x - (-5))^2 + (y - 2)^2 = 4^2
\]
This simplifies to:
\[
(x + 5)^2 + (y - 2)^2 = 16
\]
Thus, the correct equation describing the circle is:
**C. \((x + 5)^2 + (y - 2)^2 = 16\)**
\[
(x - h)^2 + (y - k)^2 = r^2
\]
In this case, the center of the circle is \((-5, 2)\) and the radius is \(4\).
Substituting \(h = -5\), \(k = 2\), and \(r = 4\) into the equation gives:
\[
(x - (-5))^2 + (y - 2)^2 = 4^2
\]
This simplifies to:
\[
(x + 5)^2 + (y - 2)^2 = 16
\]
Thus, the correct equation describing the circle is:
**C. \((x + 5)^2 + (y - 2)^2 = 16\)**