A hyperbola is the set of all points in the plane for which the absolute value of the difference of the distances to two fixed points [math] F_1[/math] and [math]F_2[/math] (the foci) is a constant. This constant equals the distance between the vertices of the hyperbola.[br]In the applet below points [math]L[/math], [math]M[/math] and [math]N[/math] are points on one line, so [math]| NL-NM|=LM.[/math][br][*]Drag point [math]N[/math] along the line or use the animation button to construct points from the hyperbola.[br][*]Click the checkbox to see the construction.[br][*]Drag [math]L[/math] or [math]M[/math]. What happens when [math]LM>F_1F_2[/math]?