Tracing Out A Hyperbola Using the Difference-of-The-Distances Definition
If the animation does not appear, click
here.
This animation shows how to use the difference-of-the-distances definition of hyperbola to trace out
a portion of such a curve.
(See notes below.)
The horizontal line segments that appear near the bottom of the display are
copies, colored appropriately, of the segments that connect the foci with the moving
point on the hyperbola; as the moving point traces out the curve,
the difference of the two lengths
remains constant.
Every hyperbola has two branchs, both of which have infinite extent. This animation
shows only a finite portion of the right branch of this hyperbola. The left branch
is a mirror image of the right branch, the reflection being about the mid-point of the segment
that connects the foci.
A similar figure, colored differently, lies in the plane
that appears in the
Quetelet/Dandelin argument, One More Proof of Quetelet & Dandelin,
for the ellipse.
(11/02/09)