Flag. Spiders move till distance to fly & ants is equal. Drag Fly to new place & hit flag for different parabola. "Show equidistances" puts black lines from spider to fly & ant line. Color lines are tangents of parabola and, in the same color, the perpendicular to each tangent. Fly is draggable even after lines drawn. They'll redraw.
Spiders go to spots equally distant from fly & ant line. In math terms, ant line is "directrix" and the fly is the "focus" point. The parabola is the set of points equally distant from directrix and focus. As if spiders are attracted equally to fly and ant lines.
