Find the center and radius of the circle. \[ x^{2}+(y-8)^{2}=64 \] The center of the circle is \( (0,8) \). (Type an ordered pair.) The radius is \( \square \). (Simplify your answer. Type an exact answer, using radicals as needed.)

To find the center and radius of the circle given by the equation \[ x^{2}+(y-8)^{2}=64, \] we can compare this equation to the standard form of a circle's equation, 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: - The term \(x^{2}\) indicates that \(h = 0\) (since there is no \((x - h)\) term). - The term \((y - 8)^{2}\) indicates that \(k = 8\). - The right side of the equation is \(64\), which represents \(r^{2}\). Thus, we can identify: - The center of the circle is \((h, k) = (0, 8)\). - To find the radius \(r\), we take the square root of \(64\): \[ r = \sqrt{64} = 8. \] So, the center of the circle is \[ (0, 8) \] and the radius is \[ 8. \] In summary: - The center of the circle is \((0, 8)\). - The radius is \(8\).