Parallel Chords in Ellipse

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet.

What if applet does not run?

The applet illustrates the Euclidean construction of a center of an ellipse by ruler and compass. (The blue lines can be dragged by their end- and midpoints. Just try!)

Cross the ellipse by two parallel lines AB and CD, with points A, B, C, D on the ellipse. Find the midpoints M and N of the segments AB and CD. Line MN is incident to the center of the ellipse. Therefore by choosing a pair of parallel lines with a different direction, the center of the ellipse is found at the intersection of the two midlines.

The construction works for ellipse just because it works for a circle. Indeed, an ellipse is a projection of a circle along one of its axes. Such a transformation maps straight lines on straight lines, preserves line and point incidence and relative lengths of segments on the same line; so that it also preserves midpoints of line segments.

This same construction works for hyperbola as well and, in a sense, for parabola. Except that, for parabola, the center lies at infinity and, as a result, line MN is parallel to the axis of parabola - another line that goes through the same point at infinity.

There is an alternative construction that first draws the tangents to the ellipse.

Conic Sections > Ellipse

Pascal and Brianchon Theorems

|Activities| |Contact| |Front page| |Contents| |Geometry|

Copyright © 1996-2018 Alexander Bogomolny