A parabola is the set of points
equidistant from a line, called the directrix, and a fixed
point called the focus. With
a few construcions one creates a setup like the following:
If we allow the midpoint of the horizontal
line to move from left to right, a parabolic pattern is created
by the attached midpoint's segment.
Click here to view the image
One should notice the following
When one uses a trace feature one can explicitly
see the parabola.
Click here to see an
additional trace feature trace in action
You should notice something like the following
Finally we examine
the Locus command and watch how a movement of a few basic
objects drags the parabola anywhere.