Parabolic Constructions

When discussing a parabola, some definitions are in order. These are:

Parabola: this is the locus of all points whose distances from a fixed point equal their distances from a fixed line.

Locus: the set of all points equidistant from both the directrix and the focus.

Directrix: the fixed line in the construction of a parabola.

Focus: the fixed point in the construction of a parabola.

Vertex: a point constructed via a perpendicular line from the focus directly to the directrix. It is the point of intersection of the locus and perpendicular line.

Click on "Parabola" to view and observe its movement.

One way to view the parabola is to watch the locus form using an action button as done previously; another way is to watch the trace of the tangent line at the constructed point:

Click on Trace of Tangent Line

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The next construction is to generate a parabola with the 'Locus' command from the construct menu. This is done by:

1) Constructing a focus (F) and a directrix with a random point (the Driver).

2) Construct a segment from the focus to the random point (not one of the points used to create the directrix); construct a midpoint and a perpendicular bisector.

3) Construct a perpendicular bisector through the random point (driver) and mark the intersection of the two perpendicular bisectors. This intersection is a point (Driven object). Highlight the driver and then the driven object; go to the menu and choose 'locus'.

Another way of constructing a locus is to use the tangent line as the driven object. All else is the same as above: