In the applet below you can experiment with the locus definition of a hyperbola: the locus of points, P, such that the difference of the distances from two fixed points, called the foci , is constant.
Drag D below and observe the path that F follows. After points have been traced, clicking the red X in the bottom right corner will erase the traced points.
In 7.5U you experimented with waxed paper models of a parabola and an ellipse. You were asked to change the model for an ellipse to create a new locus. Let's take a look at it below.
C is the point that you would draw outside the waxed paper circle. When the waxed paper is folded so that C is on the circumference, D is the point on the line that corresponds to C. You can move the point D to get new locations of the fold line. The motion of D can be animated by using the animate button. By tracing the fold line you get the pattern that would emerge on the waxed paper. After tracing has started, the red X at the bottom right can be clicked to erase any traced lines.
Hyperbolas arise in many places in real life. The applet below simulates waves from two sources interfering. The thick circles represent crests, and the thin circles represent troughs. When a crest and trough meet, total destructive interference occurs and the net result is a "flat" area. Notice the shape of the flat areas traced out as the waves progress. The sketch can be animated or moved manually by pulling the point labelled move.
The sketches on this page were created using a prototype of JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright ©1990-1998 by Key Curriculum Press, Inc. All rights reserved. Portions of this work were funded by the National Science Foundation (awards DMI 9561674 & 9623018).