The equation of a circle is given in standard form. Complete parts a through c to follow the step by step process to sketch the graph of the circle. \[ (x-3)^{2}+(y+5)^{2}=16 \] a) Determine the center and radius of the circle. The center of the circle is \( (3,-5) \). (Type an ordered pair.) The radius is (Simplify your answer. Type an exact answer, using radicals as needed.)

To determine the center and radius of the circle given by the equation \[ (x-3)^{2}+(y+5)^{2}=16, \] we can identify the center and radius from the standard form of a circle's equation, which is \[ (x-h)^{2}+(y-k)^{2}=r^{2}, \] where \((h, k)\) is the center and \(r\) is the radius. ### a) Center and Radius 1. **Center**: From the equation, we can see that \(h = 3\) and \(k = -5\). Therefore, the center of the circle is \[ (3, -5). \] 2. **Radius**: The right side of the equation is \(16\), which is equal to \(r^{2}\). To find the radius \(r\), we take the square root of \(16\): \[ r = \sqrt{16} = 4. \] ### Summary of Part a: - The center of the circle is \((3, -5)\). - The radius is \(4\). ### Answers: - The center of the circle is \( (3, -5) \). - The radius is \( 4 \).