Envelope Command

Envelope[ <Path>, <Point> ]

Creates the envelope equation of a set of output paths while the moving point is bound to another object.

An envelope is a curve that is tangent to each member of the family of the output paths at some point.

Example:

A ladder is leaning against the wall and sliding down.

The contour of its trace will be the envelope of the ladder. Strictly speaking, GeoGebra computes the envelope of the entire line containing the ladder as a segment. Only such envelopes can be computed where the appropriate construction leads to an algebraic equation system.

Note: See also Locus, LocusEquation commands and GeoGebra Automated Reasoning Tools: A Tutorial.