Euclidean Construction of Center of Ellipse
|What if applet does not run?|
The applet illustrates the Euclidean construction of a center of an ellipse by ruler and compass.
Choose any two points on Ellipse (A and B in the applet). It takes just a ruler and a drawing of a few lines to find the tangents to the ellipse at A and B. Assume the tangents meet at point S. Let M be the midpoint of AB. As a matter of fact line SM passes through the center of the ellipse. So to find the center one needs to repeat the construction for an additional pair of two points. The two lines SM will meet at the center.
The construction works for ellipse just because it works for a circle. Indeed, an ellipse is a projection of a circle. Projective transformations map straight lines on straight lines, preserve line and point incidence and relative lengths of segments of the same line; so that they also preserve 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 SM is parallel to the axis of parabola - another line that goes through the same point at infinity.
There is an alternative construction that draws a line through the midpoints of two parallel chords in ellipse.
Conic Sections > Ellipse
- What Is Ellipse?
- Analog device simulation for drawing ellipses
- Angle Bisectors in Ellipse
- Angle Bisectors in Ellipse II
- Between Major and Minor Circles
- Brianchon in Ellipse
- Butterflies in Ellipse
- Concyclic Points of Two Ellipses with Orthogonal Axes
- Conic in Hexagon
- Conjugate Diameters in Ellipse
- Dynamic construction of ellipse and other curves
- Ellipse Between Two Circles
- Ellipse in Arbelos
- Ellipse Touching Sides of Triangle at Midpoints
- Euclidean Construction of Center of Ellipse
- Euclidean Construction of Tangent to Ellipse
- Focal Definition of Ellipse
- Focus and Directrix of Ellipse
- From Foci to a Tangent in Ellipse
- Gergonne in Ellipse
- Pascal in Ellipse
- La Hire's Theorem in Ellipse
- Maximum Perimeter Property of the Incircle
- Optical Property of Ellipse
- Parallel Chords in Ellipse
- Poncelet Porism in Ellipses
- Reflections in Ellipse
- Three Squares and Two Ellipses
- Three Tangents, Three Chords in Ellipse
- Van Schooten's Locus Problem
- Two Circles, Ellipse, and Parallel Lines
Copyright © 1996-2017 Alexander Bogomolny