The hyperbola as a locus.
The hyperbola is the locus of all points the difference of whose distances from two fixed points is a constant. We visualize this definition and check that difference when moving in a hyperbola.
Move R to check that the difference of distances is a constant. Moving a and b you are modifying the shape of the hyperbola. Complete the construction to visualize the definition in the left branch of the hyperbola.