Last modified on January 6, 2016
Graphing Calculator 3.5 or 4.0, Geogebra, or Desmos is suggested for these investigations. Some of them could be done with a TI-83 or similar hand-held technology. Or, for a challenge, try making the graphs with Excel.
- When a and b are equal, and k is an integer, this is one textbook version of the " n-leaf rose."
- Compare with
for various k. What if . . . cos( ) is replaced with sin( )?
2. Investigate -- varying a, b, c, and k.
Note: The parameter k is called the "eccentricity" of these conics. It is usually called "e" but for many software programs e is a constant and can not be set as a variable.
For notes on a derivation of these formulas, click here.
5. Some interesting graphs --
when a is small, e.g. a = .1
for suitable a and range of
Replace the '10' with n and animate for some appropriate range.
(Note: some of these graphs may become more interesting -- or disasters -- when is replaced by some function of .)