### Overview of process

Below are pictures showing how to create a large ellipse (half of one but can also be used to draw a full ellipse). I used this technique to make arc sections in a set of bookcases. No complicated jig to build; just a board, clamp and stick with slot for pencil and nail to set minor axis length.

### The Mathematics

The Y Axis represents a guide board perpendicular to board upon which you want to draw the ellipse.

- Segment E1E3 is the stick used in the operation
- Point E2 is where the nail is placed
- Point E3 is the notch for the pencil.
- See diagram below for an illustration.

and

and from geometry

Using these as parametric equations and eliminate the angle and we get equation of an ellipse:

Illustration on coordinate system

Page where you can simulate the drawing of the ellipse with different parameters.