Circle Equation: Center NOT (0,0)

Experiment with the interactive visualization below and answer the questions that appear below the applet. Note: To drag with circle without changing its radius, simply drag the circle itself (and not the points on the circle).
Questions: 1) Suppose P(x,y) = any point that lies on a circle with center (3, 4) and radius 4. Use what you've observed to write an equation that expresses the relationship among x, y, and r. (No need to square any binomial expressions.) 2) What is the equation of a circle with center (-1, 5) and radius r = 9? (No need to square any binomial expressions.) 3) Suppose another circle has center (-2, -8). Suppose this circle also passes through the point (4, 0). Write the equation of this circle. (Again, don't square any binomial expressions.) (HINT: How can we find the radius using our given information?)