Green, Red, Black

Author:
Scrooge
Topic:
Parabola
This construction contains two ways of constructing the same locus, which I think is the set of points with the same distance from a parabola and its focus point, until it crosses itself, so I mean the waterdrop-shape without its continuation. This is a demonstration that once you can make loci from simple elements (like points, lines and circles), for example, conics (like ellipses, parabolas and hyperbolas), then you can also use these secondary shapes as paths to make even more complex loci like this waterdrop-shape.
Exercise 1: can you make a locus of just the waterdrop-shape? How can you construct it? Exercise 2: can you prove it that this waterdrop-shape is really the set of points with the same distance from a parabola and its focus point?