9. 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.

Click here to view the animation in GSP. Notice that no matter where you move the focus in the GSP window, the points on the parabola remain equidistant from the directrix and the focus.

b. Repeat 9a with a trace of the tangent line at the constructed point.

Click here to view the tracing in GSP.

c. Use the locus command to generate the parabola from a constructed point or the tangent line at that point.

Click here to view the parabola.