two clocks in k/n time !

Two 'clocks' - one turning at k revolutions/unit time, the other turning at n revolutions per unit time - The BLUE point tracks the vertical position of the hand on one clock and the horizontal position of the hand on the other. Use the ORANGE dots to set the initial positions of the hands. Can you make the BLUE dot trace a - - circle - ellipse - straight line w/ positive slope - straight line w/ negative slope - parabola - more complex figures conjectures ? proofs? extensions ? What questions could/would you pose to your students based on this applet ?