Find the center and radius of the circle. \[ (x-3)^{2}+(y+5)^{2}=16 \] The center of the circle is \( (3,-5) \) (Type an ordered pair.) The radius is

The equation of the circle is given by \[ (x-3)^{2}+(y+5)^{2}=16. \] In the standard form of a circle's equation, \((x-h)^{2}+(y-k)^{2}=r^{2}\), the center of the circle is \((h, k)\) and the radius is \(r\). From the given equation: - The center \((h, k)\) can be identified as \((3, -5)\). - The right side of the equation, \(16\), represents \(r^{2}\). To find the radius \(r\), we take the square root of \(16\): \[ r = \sqrt{16} = 4. \] Thus, the center of the circle is \((3, -5)\) and the radius is \(4\). In summary: - The center of the circle is \((3, -5)\). - The radius is \(4\).