LocusEquation (explicit)
LocusEquation[E,M] computes the equation of the set of possible locus points E while M is running on the path d. It must be a parabola by geometrical definition. (Alternatively, it can be shown that the curve is geometrically similar to the graph of function .) One can study a family of equations while the directrix d and focus point F change their values by dragging: they are bivariate quadratic equations.