Two parametric curves

This applet plots two simultaneous parametric curves. Do the two points collide?

There are two particles, red and blue. Enter the parametric equations for their paths in the boxes. Drag the slider for t to see the points move.

Do the particles collide? What happens when they do?

Do the paths intersect? Does this always mean that the particles will collide?

Other resources:

Geogebratube page for this applet

One parametric curve applet