Introduction

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 a line. Construct a parabola given a fixed point for the focus and a line (segment) for the directrix. Therefore, to construct parabola on GSP, we need to start with a focus and a directrix as shown below.

First construct a point on the directrix. Then construct a perpendicular line to the directrix through this point.

Then, construct a segment from the focus to the point on the directrix. Then construct the midploint of this segment.

Construct a perpendicular line to the segment you constructed through its midpoint. Construct the intersection point it makes with the line perpendicular to the directrix.

You can use an Action Button to generate the parabola from an animonition and trace. Click here for a GSP file to view and explore the trace of the tangent point of a parabola.

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