Parabolas

By

Brooke Norman

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 parabola generally looks like:

In this section, the Action Button is going to be used to generate the parabola from an animation and trace of a constructed point.

Click here to see the animation, using 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.

Now, we are going to do the same as above, only this time we are going to trace the tangent line at the constructed point.

Click here to see the trace, using GSP.

Finally, we are going to use the locus command to generate the parabola from a constructed point to the tangent line at that point.

Click here to see the parabola.

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