"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."
This investigation will use Geometer’s Sketchpad to:
a. Use an Action Button to generate the parabola from an animation and trace of a constructed point. Click here to see animation (a)!
b. Repeat 9a with a trace of the tangent line at the constructed point. Click here to see animation (b)!
c. Use the locus command to generate the parabola from a constructed point or the tangent line at that point. Click here to see (c)!
I also created a locus from a fixed point and a circle, here.
And, locus of a circle using the center of another circle, here.