A quadratic locus equation in GeoGebra by using the synthetic definition. Dynamic coordinates.
[list=1] [*]In Step 1 we create three free points A', B' and C'. They should be hidden in the final version of the applet, but for the explanation we just used gray color here. [*]In Step 2 commands like [b]A=DynamicCoordinates[A',round(x(A')),round(y(A'))][/b] were used to set up constraints for points A, B and C. [*]In Step 3-4 we define line a and put point D on line a. Then in Steps 5-6 point E is constructed by Euclidean steps (as previously). [*]Now the locus of point E while point D is moving on line a, is to be defined (Step 7, as previously). [*]Finally in Step 8 we obtain the equation of the locus. [*]Now we can also hide points A', B' and C' by right-clicking on them and disable the Show Object option. [/list]