Quadratic Bezier curve is a parabolic segment

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This sketch shows a geometric proof that the quadratic Bezier curve is also a parabolic segment. The radii of the circle connect the focus and directrix to a point on the curve. The distances from the focus and directrix to the plotted point are always equal.

Points A and C are the endpoints of the Bezier curve. Point B is the control point.

• Move points A, B and C to change the shape of the triangle and curve.
• Move point D to trace the locus of point H.

Click here to download the worksheet. Note: you do not need to extract the contents of the Zip file. Simply change the extension from ".zip" to ".ggb" and it will work. You can download an old Geometer's Sketchpad version of this worksheet, here.

Created by Michael Horvath using GeoGebra. Last modified: Monday, 08-Dec-08 13:27:15 PST

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