Find the center and radius of the circle given by x^2 + y^2 - 6x + 8y - 11 = 0.

Step 1: Group the x-terms and y-terms.

Start with:
x^2 + y^2 - 6x + 8y - 11 = 0

Move the constant to the right side and group related terms:
(x^2 - 6x) + (y^2 + 8y) = 11

Step 2: Complete the square for the x-terms.

For x^2 - 6x, take half of -6 and square it:
(-6/2)^2 = (-3)^2 = 9

Add 9 to both sides.

Step 3: Complete the square for the y-terms.

For y^2 + 8y, take half of 8 and square it:
(8/2)^2 = 4^2 = 16

Add 16 to both sides.

The equation becomes:
(x^2 - 6x + 9) + (y^2 + 8y + 16) = 11 + 9 + 16

Step 4: Rewrite the perfect-square trinomials.

x^2 - 6x + 9 = (x - 3)^2

y^2 + 8y + 16 = (y + 4)^2

So:
(x - 3)^2 + (y + 4)^2 = 36

Step 5: Compare with the standard equation of a circle.

The standard form is:
(x - h)^2 + (y - k)^2 = r^2

Comparing the equations gives:
h = 3
k = -4
r^2 = 36

Therefore:
r = 6

So the center is (3, -4) and the radius is 6.