LocusEquation Command

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LocusEquation[ <Locus> ]
Calculates the equation of a Locus and plots this as an Implicit Curve.
LocusEquation[ <Point Creating Locus Line Q>, <Point P> ]
Calculates the equation of a Locus by using inputs tracer point Q and mover point P, 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 P attached to d (the mover point), then create line p as a perpendicular line to d through P. Also create line b as bisector of points F and P. Finally, point Q (the point creating locus line) is to be created as intersection of lines p and b. Now LocusEquation[Q,P] 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.
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