Hyperbola as Envelope
- Michael Ortiz
Suppose we have two points F and G in the exterior of a circle, with the center O as midpoint. Given any point P on the circle, the line perpendicular to FP at P is tangent to the hyperbola with foci F and G and auxiliary circle O. Similarly for G. This allows us to construct a hyperbola as an "envelope" of tangents. In the applet below, the auxiliary circle and foci are shown in white. The rays from the focus are shown in yellow, and the tangents are shown in green. The number of tangents constructed varies from 0 to 180.