For the equation \( x^{2}+y^{2}-2 x-4 y-20=0 \), do the following. (a) Find the center \( (h, k) \) and radius \( r \) of the circle. (b) Graph the circle. (c) Find the intercepts, if any. (a) The center is (Type an ordered pair.)

To find the center and radius of the circle represented by the equation \( x^{2}+y^{2}-2 x-4 y-20=0 \), we can rewrite it in the standard form. 1. First, we rearrange the equation: \[ x^{2} - 2x + y^{2} - 4y = 20. \] 2. Next, we complete the square for \( x \) and \( y \). - For \( x^{2} - 2x \): - Take half of -2, square it: \((-1)^{2}=1\). - Add and subtract 1: \( (x^2 - 2x + 1) - 1 = (x - 1)^{2} - 1 \). - For \( y^{2} - 4y \): - Take half of -4, square it: \((-2)^{2}=4\). - Add and subtract 4: \( (y^2 - 4y + 4) - 4 = (y - 2)^{2} - 4 \). 3. Incorporating these into the equation gives: \[ (x - 1)^{2} - 1 + (y - 2)^{2} - 4 = 20. \] 4. Simplifying results in: \[ (x - 1)^{2} + (y - 2)^{2} = 25. \] Now we can identify the center and radius: - Center \((h, k) = (1, 2)\) - Radius \(r = 5\) (since \( r^2 = 25\)). (a) The center is \( (1, 2) \).