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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Conic5Points

Two points determine a line, three a circle, and it takes five points to determine a conic. In this sketch, the 5 points are *A*, *B*, *C*, *D*, *E*. Drag these points, and you'll see their conic.
This construction is based on a theorem that Pascal discovered while a teenager. The conic is sketched as the locus of the point *F*.

As you drag the 5 points, why do you see lots more ellipses and hyperbolas (with asymptotes) than parabolas?

If 4 of the points are vertices of a rectangle, where must the 5th point be in order for the conic to be an ellipse?

For more, see **GEOMETRY IN ACTION**, Chapter 7.