You can see the equation of the parabola defined by the directrix (line [i]AB[/i]) and the focus point [i]F[/i].
[list=1] [*]Drag point [i]F[/i] to change the focus of the parabola. [*]Drag points [i]A[/i] and [i]B[/i] to change the directrix of the parabola. [*]Try to find positions for [i]F[/i], [i]A[/i] and [i]B[/i] to get "short" equations. [*]Can you set up the construction to not see the parabola any longer? [*]Can you collect common properties of all displayed equations? (Collect the variables and the degree of the expressions.) [/list]