LocusEquation Command

LocusEquation[ <Locus> ]

Calculates the equation of a Locus and plots this as an Implicit Curve

LocusEquation[ <Locus Point>, <Moving Point> ]

Calculates the equation of a Locus and plots this as an Implicit Curve

Example:

Let us construct a parabola as a locus: Create free points A and B, and line d lying through them (this will be the directrix of the parabola). Create free point F for the focus. Now create constrainted point M attached to d (the mover point), then create line p as a perpendicular line to d through M. Also create line b as bisector of points F and M. Finally, point L (the locus point) is to be created as intersection of lines p and b. Now LocusEquation[L,M] will yield the locus equation which will be the implicit curve of the defined parabola.

Note: See also Locus command.

Note:

• Works only for a restricted set of geometric locus, i.e. using points, lines, circles, conics.
• If the locus is too complicated then it will return 'undefined'.
• The calculation is done using Gröbner bases, so sometimes extra branches of the curve will appear that were not in the original locus.
• The equation is computed by using the built in Reduce/Cali subsystem in GeoGebra 4.2. In GeoGebra 5.0 and above the Singular WebService is used if the remote server appears to be fast enough to use it for consecutive calculations, otherwise GeoGebra falls back to use Reduce/Cali (this can be forced by disabling the Singular WebService by using command line option --singularWS=enable:false).