A quadratic locus equation in GeoGebra. We construct the parabola by using the synthetic definition.

In Steps 1 and 2 line AB (denoted by "a") and point C are defined.

In Step 3 we put point D on line a. Then in Steps 4-5-6 point E is constructed by Euclidean steps.

Now the locus of point E while point D is moving on line a, is to be defined (Step 7).

Finally in Step 8 we obtain the equation of the locus.

Under some systems and conditions the computation may be fast enough, thus the animation will not be fluent. A simple way to avoid some computations is to narrow the available inputs to grid points. To do that, select Options > Point Capturing > Fixed to Grid.
Now point D is also constrained to grid points, unfortunately. This behavior can, however, be improved. Turn on the next page to see how.