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 (Type an ordered pair.)

Given the equation of the circle in standard form: \((x-3)^{2}+(y+5)^{2}=16\). a) To determine the center and radius of the circle, we compare the given equation with the standard form of the equation of a circle: \((x-h)^{2}+(y-k)^{2}=r^{2}\), where \((h,k)\) is the center of the circle and \(r\) is the radius. Comparing the given equation with the standard form, we can see that: - \(h = 3\) - \(k = -5\) - \(r = \sqrt{16} = 4\) Therefore, the center of the circle is at the point \((3, -5)\) and the radius of the circle is 4 units.