LocusEquation Command

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 P on Line d (the mover point), then create line p as a perpendicular line to d through P. Also create line b as perpendicular bisector of Line Segment FP. Finally, point Q (the point creating locus line) is to be created as intersection of Lines p and b. Now LocusEquation[Q,P] will find and plot the exact equation of the locus.

Note: See also Locus command.

Note:

• Works only for a restricted set of geometric loci, i.e. using points, lines, circles, conics. [Rays and line segments will be treated as (infinite) lines]
• 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.