What is an ellipse?

An ellipse is what you see when you look at a circle from an angle.

EllipseRotated

You can draw an ellipse by using two push pins, a pencil, and a piece of string. Stick the two pins into a piece of cardboard or some other appropriate flat surface. The string should be longer than the distance between the two pins. Tie one end of the string to each pin, and stretch the string with the pencil, and draw a curve by moving the pencil while keeping the string tight. You should get a curve similar to the one in the following picture.

ellipseThe two pins are located at the points labeled Focus. The length of the brown line segment is the total length of the string. Note that the length of the green line segment plus the length of the blue line segment is always equal to the length of the brown line segment.

An ellipse is called a conic section because it can be generated as a slice of a cone. Other conic sections include hyperbolas and parabolas.

conic

The planets follow elliptical orbits with the Sun at a focus. See http://en.wikipedia.org/wiki/Apsis for a picture.

An ellipse can also be defined in terms of an equation or parametric equations.