Reeves Henry
08/04/2023 · Elementary School
Find the center and radius of the circle. \[ (x+3)^{2}+(y-4)^{2}=26 \] The center of the circle is \( (-3,4) \). (Type an ordered pair.) The radius is \( \square \). (Simplify your answer. Type an exact answer, using radicals as needed.)
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Step-by-step Solution
The equation of the circle is given by
\[
(x+3)^{2}+(y-4)^{2}=26.
\]
This equation is in the standard form of a circle, which is
\[
(x-h)^{2}+(y-k)^{2}=r^{2},
\]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
From the given equation, we can identify:
- The center \((h, k)\) is \((-3, 4)\).
- The right side of the equation, \(26\), represents \(r^{2}\).
To find the radius \(r\), we take the square root of \(26\):
\[
r = \sqrt{26}.
\]
Thus, the center of the circle is
\[
\boxed{(-3, 4)}
\]
and the radius is
\[
\sqrt{26}.
\]
Quick Answer
The center of the circle is \((-3, 4)\) and the radius is \(\sqrt{26}\).
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