**Carrie Dillman**
This is an investigation of the construction of a parabola.
I have started with a line, the directrix, a point on the line, and a point
in the plane not on the directrix, the focus. The parabola consists of the set
of points equidistant from the focus and directrix. Click on the animate button
to check it out.

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Parabola

The same parabola can be created by tracing the lines
tangent to every point in the set of points creating the parabola.

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Tangent Line

Using the locus command under the construct menu in Geometer's
Sketchpad, I have created the set of all points of a parabola. Move the focus
around and see the infinite number of possible parabolas. Don't forget to move
it under the directrix!

This page uses **JavaSketchpad**, a World-Wide-Web component of *The Geometer's Sketchpad.* Copyright © 1990-2001 by KCP Technologies, Inc. Licensed only for non-commercial use.

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Locus

Below I have used the locus command again to create not only
a parabola, but also an ellipse, and hyperbola. As you can see, I have used
the Greek construction rules to create these conics. Note for a parabola, the
distance of PF (point to focus) equals the distance PD (point to directrix).
You've probably noticed the circles in this construction. The original circle
used to construct the parabola is controlled by the slider in the top left corner.
I constructed the ellipse using a circle 1/2 the size of the circle used to
construct the parabola. I constructed the hyperbola using a circle 2 times the
size of the circle used to construct the parabola. 1/2 and 2 are the eccentricities
of these equations.

PF=PD ==> gives a parabola

PF=1/2PD ==> gives an ellipse

PF=2PD ==> gives a hyperbola

This page uses **JavaSketchpad**, a World-Wide-Web component of *The Geometer's Sketchpad.* Copyright © 1990-2001 by KCP Technologies, Inc. Licensed only for non-commercial use.

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Conics