[color=#000000]Experiment with the interactive visualization below and answer the questions that appear below the applet.[br][br][/color][i][color=#000000]Note: To drag with circle without changing its radius, simply drag the circle itself [br] (and not the points on the circle). [/color][/i]

[color=#980000][b]Questions: [/b][/color] [br][br][color=#000000]1) Suppose [i]P(x,y)[/i] = 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 [i]x[/i], [i]y[/i], and [i]r[/i]. [br] (No need to square any binomial expressions.) [br][br]2) What is the equation of a circle with center (-1, 5) and radius [i]r[/i] = 9? (No need to square any binomial expressions.) [br][br]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?)[br][/color]