Quadratic Bezier Curve as Parabolic Segment

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 AB and C to change the shape of the triangle and curve.
  • Move point D to trace the locus of point H.