What is the radius of x^2 + y^2 - 2x - 4y - 31 = 0

First we have to complete the square on both the x and y terms. Move the 31 to the right side.

x^2 - 2x + y^2 - 4y = 31

x^2 - 2x + 1 + y^2 - 4y + 4 = 31 + 1 + 4

(x - 1) ^2 + (y - 2) ^2 = 36

36 = r^2

r = 6