Maxwell Davies
07/25/2023 · Elementary School
Find the center and radius of the circle. \[ (x-3)^{2}+(y+5)^{2}=16 \] The center of the circle is (Type an ordered pair.)
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Step-by-step Solution
The equation of the circle is given in the standard form:
\[
(x - h)^2 + (y - k)^2 = r^2
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
From the equation:
\[
(x - 3)^2 + (y + 5)^2 = 16
\]
we can identify the following:
- \(h = 3\)
- \(k = -5\)
- \(r^2 = 16\)
To find the radius \(r\), we take the square root of \(r^2\):
\[
r = \sqrt{16} = 4
\]
Thus, the center of the circle is:
\[
(3, -5)
\]
So, the center of the circle is \(\boxed{(3, -5)}\).
Quick Answer
The center of the circle is \((3, -5)\).
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