MacLaurin's Construction of Conics

Let ABC be a variable triangle which is such that the vertices B and C respectively move on two given lines l and m, and the sides BC, CA, and AB respectively pass through given points U, V, and W. Then the locus of the vertex A is a conic. If points U, V, W, are collinear then the locus degenerates into a straight line concurrent with l and m.


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 https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.


What if applet does not run?

Proof

Conics

 64640335