Quadratic Bezier Curve as 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.

Download the worksheet here. Download an older Geometer's Sketchpad version of this worksheet here.

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This page © Copyright 2009 Michael Horvath. Last modified: May 30 2010 08:02:45.