Difference between revisions of "LocusEquation Command"
From GeoGebra Manual
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;LocusEquation[ <Point Creating Locus Line Q>, <Point P> ] | ;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. | :Calculates the equation of a Locus by using inputs tracer point ''Q'' and mover point ''P'', and plots this as an Implicit Curve. | ||
| − | {{example| 1=<div>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 <code><nowiki>LocusEquation[Q,P]</nowiki></code> will find and plot the exact equation of the locus.</div>}} | + | :{{example| 1=<div>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 <code><nowiki>LocusEquation[Q,P]</nowiki></code> will find and plot the exact equation of the locus.</div>}} |
| − | {{ | + | :{{Notes|1=<br> |
| − | + | :*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] | |
| − | * 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'. |
| − | * If the locus is too complicated then it will return 'undefined'. | + | :*The calculation is done using [[w:Gröbner_basis|Gröbner bases]], so sometimes extra branches of the curve will appear that were not in the original locus.<hr> |
| − | * The calculation is done using [[w:Gröbner_basis|Gröbner bases]], so sometimes extra branches of the curve will appear that were not in the original locus.}} | + | ::See also [[Locus Command|Locus]] command. |
| + | }} | ||
{{betamanual|version=5.0|1= | {{betamanual|version=5.0|1= | ||
{{Note|1= | {{Note|1= | ||
In GeoGebra 5 and above a remote web server may be used to perform the calculation (this can be disabled by using command line option <code><nowiki>--singularWS=enable:false</nowiki></code>).}}}} | In GeoGebra 5 and above a remote web server may be used to perform the calculation (this can be disabled by using command line option <code><nowiki>--singularWS=enable:false</nowiki></code>).}}}} | ||
Revision as of 21:59, 1 February 2013
- 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.
- Notes:
- 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.
- See also Locus command.
 |
Following text is about a feature that is supported only in GeoGebra 5.0.
Note: In GeoGebra 5 and above a remote web server may be used to perform the calculation (this can be disabled by using command line option --singularWS=enable:false). |
