Parabola as Envelope
- Michael Ortiz
Suppose we have a point F and a line m. Given any point P on m, the line perpendicular to FP at P is tangent to the parabola with focus F and directrix parallel to m and twice as far from F. This allows us to construct a parabola as an "envelope" of tangents. In the applet below, the initial line and the focus are shown in white. The rays from the focus are shown in green, and the tangents are shown in yellow. The number of tangents constructed varies from 2 to 200.