  GeoGebra is an open source mathematics education software tool being used in
thousands of schools worldwide. Since version 4.2 (December 2012) it supports
symbolic computation of locus equations as a result of joint effort of
mathematicians and programmers helping the GeoGebra developer team. The joint
work, based on former researches, started in 2010 and continued until present
days, now enables fast locus and envelope computations even in a web browser in
full HTML5 mode. Thus, classroom demonstrations and deeper investigations of
dynamic analytical geometry are ready to use on tablets or smartphones as well.
  In our paper we consider some typical secondary school topics where
investigating loci is a natural way of defining mathematical objects. We
discuss the technical possibilities in GeoGebra by using the new commands
LocusEquation and Envelope, showing through different examples how these
commands can enrich the learning of mathematics. The covered school topics
include definition of a parabola and other conics in different situations like
synthetic definitions or points and curves associated with a triangle. Despite
the fact that in most secondary schools, no other than quadratic curves are
discussed, simple generalization of some exercises, and also every day
problems, will smoothly introduce higher order algebraic curves. Thus our paper
mentions the cubic curve "strophoid" as locus of the orthocenter of a triangle
when one of the vertices moves on a circle. Also quartic "cardioid" and sextic
"nephroid" can be of every day interest when investigating mathematics in, say,
a coffee cup.
  We also focus on GeoGebra specific tips and tricks when constructing a
geometric figure to be available for getting the locus equation. Among others,
simplification and synthetization (via the intercept theorem) are mentioned.
