Locus of
Equidistant Points
A parabola is the set of points
equidistant from a line, called the directrix, and a fixed point,
called the focus. Assume the focus is not on the line. Construct
a parabola given a fixed point for the focus and a line (segment)
for the directrix.
a. Use an Action Button to generate the parabola
from an animation and trace of a constructed point.
b. Use an Action Button to generate the
parabola from an animation and trace of the tangent line at the
constructed point.
c. Use the locus
command to generate the parabola from a constructed point
or the tangent line at that
point.
Repeat the parabola construction but use a
circle as the "directrix." Let F be any point in the
plane other than the center of the circle. Assume F is not on
the circle; it can be either inside or outside.
Use the Action
Button to generate the set of points equidistant from a fixed
point F and a circle.
Use the
locus command to generate the same set of points.