Circles are special cases of ellipses, obtained when the cutting plane is perpendicular to the cone's axis. An ellipse is also the locus of all points of the plane whose distances to two fixed points add to the same constant.
A circle has one center, called a focus, but an ellipse has two foci.
An ellipse is simply all points on a graph that the sum of the distances from 2 points are the same. For example, an ellipse can be made by putting two pins into cardboard and a circle of string around those two, then putting a pencil in the loop and pulling as far as possible without breaking the string in all directions. The orbits of the planets are ellipses, with the sun at one focus and nothing at the other.
The equation of an ellipse is :
where the center of the ellipse is (h,k). 2A is the length from each end of the longer skinnier side. 2b is the length of the 2 ends of the short side. A²-B²=C² for c is the length between the foci and the center.
- Ellipse & Hyperbola Construction - An interactive sketch showing how to trace the curves of the ellipse and hyperbola. (Requires Java.)
- Ellipse Construction - Another interactive sketch, this time showing a different method of tracing the ellipse. (Requires Java.)
- Ellipse on MathWorld - More on Ellipse
- The Shape and History of The Ellipse in Washington, D.C. by Clark Kimberling
- Collection of animated ellipse demonstrations. Ellipse, axes, semi-axes, area, perimeter, tangent, foci.
- Woodworking videos showing how to work with ellipses in wood.