PDST Locus Of Double Branch Hyperbola

Recall that a hyperbola is a locus (set) of points in the plane for which the difference of the distances from two fixed points, called foci, remains constant.   In the applet below, feel free to adjust the black siders and the location of the brown point (x,y) on the hyperbola before dragging the blue slider.   What is the value of this special difference?