Parametric Ellipses

Use the sliders to adjust the constants a, b, c, and d in the family of parametric functions. Once you've found the values you want, clear the screen (either zoom out and in, or right click on the drawing pad, select "properties" and click ok. If you open the applet in Geogebra, you can also clear the screen with "control+F") Then slide t from 0 to 20, observing not only the path of the dot, but also its motion.

1. Make a circle with radius = 3, centered at (3, -2). What are the values of a - d?
2. Make the same circle, but have it traverse the path in the opposite direction (counter-clockwise or clockwise, depending on the answer to #1.) Now what are the values of a - d?
3. Make an ellipse with widest x-extent = 5 and widest y-extent = 2, centered at (1, 2). (These will eventually be called "major axis length" and "minor axis length.")
4. Make a vertical line segment from (-2, -3) to (-2, 3).
5. Make an horizontal line segment from (-1, 4) to (3, 4).

Dave Matthews, April 2, 2007, Created with GeoGebra