Find the center and radius of the circle whose equation is $x^{2}-5 x+y^{2}+9 y+17=0$.

The center of the circle is
The radius of the circle is

Step 1 ：The general equation of a circle is given by \((x-h)^2 + (y-k)^2 = r^2\), where \((h,k)\) is the center of the circle and \(r\) is the radius. We can rewrite the given equation in this form to find the center and the radius.

Step 2 ：To do this, we complete the square for the x and y terms. The equation can be rewritten as: \((x^2 - 5x) + (y^2 + 9y) = -17\)

Step 3 ：To complete the square, we take half of the coefficient of x, square it and add it to both sides. We do the same for y. The coefficient of x is -5, half of it is -5/2 = -2.5, and its square is 6.25. The coefficient of y is 9, half of it is 9/2 = 4.5, and its square is 20.25.

Step 4 ：So, the equation becomes: \((x^2 - 5x + 6.25) + (y^2 + 9y + 20.25) = -17 + 6.25 + 20.25\)

Step 5 ：This simplifies to: \((x - 2.5)^2 + (y + 4.5)^2 = 9.5\)

Step 6 ：So, the center of the circle is \((2.5, -4.5)\) and the radius is the square root of 9.5.

Step 7 ：Let's calculate the square root of 9.5 to find the radius. radius = 3.082207001484488

Step 8 ：Final Answer: The center of the circle is \((2.5, -4.5)\) and the radius of the circle is \(\boxed{3.082207001484488}\)