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.


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