A possible classroom scenario
Technically the Relation tool and command are the easiest symbolic means. On the other hand, some teaching scenarios may require different tools to consider, or more than one tool, but in a different order than listed previously.
The workflow
- An implicit locus is computed with GeoGebra,
- a conjecture for the output curve is made by the pupil,
- the conjecture is checked by the Relation tool or command in GeoGebra,
- the proof can be optionally worked out by paper and pencil by the pupil,
- the theorem can be generalized by plotting further implicit loci with GeoGebra—as further experiments for the pupil. Actually the pupils should be allowed to "just play" with the applet, to modify it: to just try to find new, interesting relations.