1. For some positive real number r, the line x + y = r is tangent to the circle x^2 + y^2 = r. Find r.
2. Find the center of the circle passing through the points (-1,0), (1,0), and (3,1). Express your answer in the form "(a,b)."
3. A line with slope 3 is 2 units away from the origin. Find the area of the triangle formed by this line and the coordinate axes.
4. Find the maximum value of y/x over all real numbers x and y that satisfy (x - 3)^2 + (y - 3)^2 = 6.