ÒEccentricityÓ

Is that a dance move??

By: Carly Cantrell

This investigation will use a graphing software to
compare the below equations to try and figure out what ÒeccentricityÓ is all
about.

The following will be explored:

When p=1 and k=1

The graphs have shown us very similar parabolasÉ keep
that in mind!

The parabolas only differ by a determined transformation.

When p=1 and k=2

The graphs have shown us very similar hyperbolasÉ Hmmmmmm.

There are no long similar parabolas, but very similar hyperbolas.

When p=1 and k=

The graphs have shown us very similar ellipsesÉ

I am beginning to see a pattern.

Have you caught on?

Eccentricity is not a dance move.

Rather, it can be thought of as a measure of how much the conic section
deviates from being circular.

Specifically,

The eccentricity of a parabola is 1.

The eccentricity of a hyperbola is greater than 1.

And the eccentricity of an ellipse is
less than 1 but greater than 0.

What does that make the eccentricity of a circle?

Well, a circle does not deviate from a circle
very much, so it is 0.

Below are more intriguing examples:

An imporatant note: As theta was affected by 45 degrees, the ellipse roatated to sit on poles along the line y=x.