EMAT 4680/6680 Explorations 11
Polar Equations

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.


1. Investigate



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.

4. Investigate

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 .)

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