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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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 \(\boxed{(3, -5)}\).

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The center of the circle is \((3, -5)\).
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