What definition is dynamically being illustrated below? Describe.
(Feel free to change the locations of any of the points and/or the circle itself.)
Definition of a Hyperbola:
A hyperbola is a locus (set of points that satisfy a certain condition) in the plane, for which the difference of the distances from 2 other fixed points, called foci, is constant. In the applet, A and B are foci. Hyperbolas have 2 branches. This applet only traces out one of these branches.
1) Since the radius of a circle is constant, we know that AC = constant.
2) Thus, this implies AD - CD = a constant value.
3) Since p is the perpendicular bisector of the segment with endpoints B and C, we know BD = CD.
(Why?)
4) Thus, given (2) and (3), we can say that AD - BD = a constant value.
