Conic sections - hyperbola machine

The hyperbola can be described as the locus of a point that moves so that the difference of the distances of the point to the two foci is constant.

Use a hyperbola machine or the overlapping circles grid paper to investigate the above.

Can you explain why the hyperbola machine produces the locus of a point that moves so that the difference of the distances is constant?

Use this definition to produce the standard equation of the hyperbola (p118 QMaths12C).