One of the essential advantages of dynamic geometry software against pen and paper is the possibility to trace the movement of points. Though this idea did not develop through the use of computers - loci can be found in works of Gauß and other mathematicians - they now can be studied by students, teachers and other people who are not as brilliant as Gauß.
The parabola, nowadays mostly known as the graph of f(x) = x2, can be defined by giving its focus and directrix: A parabola is the set of all points Px that have the same distance to a given point P (focus) and a given line l (directrix).
A parabola can be constructed as a locus as follows:
Now you can construct the parabola with a DGS of your choice.