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After completing the Parabola Generator, I realized the Ellipse and Hyperbola could be generated with modifications to the same device. These modifications change the basic parameters that describe conic sections - the distance from the directrix to the vertex (vD) and the distance from the vertex to the focus (vF).

The eccentricity of a conic section is determined by dividing vF by vD.
  1. A value < 1 describes an ellipse.
  2. A value = 1 describes a parabola.
  3. A value > 1 describes a hyperbola.
The parabola generator was the easiest to construct because vD = vF. This relationship allowed me to use one compass to open the parallelogram and strike arcs, after moving the compass to the focus. To draw ellipses and hyperbolas, the compass setting used to open the parallelogram is different from the setting used to strike the arcs. Instead of changing the compass setting after opening the parallelogram, I decided to use two compasses for the ellipse and hyperbola generators.

To make the animations easier to draw, I used multiples of vD and vF for the compasses settings.

More Conic Section definitions are on the Hyperbola page.