- No, we cannot tell where the image of t=0 is soley by looking at the curve. For example, the function q(t)=(cos(t+Pi), sin(t+Pi)) has EXACTLY the same image (the unit circle), but the point t=0 is sent to (-1,0) instead of to (1,0).
- The vector c translates the image of the parametrized cicle by c.
- No, you can't determine velocity vectors. The function r(t)=(cos(2t), sin(2t)) has the unit circle as its image, but it traces out the circle twice as fast as the function p, therefore the velocity vectors are twice as long.
- c) The path is a helix.
- Stacking circles that are being linearly translated as they are stacked results in a "slanted cylinder" as shown below.

Last modified: Wed Oct 23 16:58:48 1996