Focus and Directrix in a Quadratic Bézier Curve

Any quadratic Bézier curve (with unit parameter ) represents a parabolic segment. This Demonstration illustrates the relationship between the disposition of the points and the vertex, locus, and directrix of the corresponding parabola.
You can drag the points , , and . The median of the triangle corresponding to the control point is perpendicular to the directrix of the parabola, but the vertex and focus are generally not on this line.
The point of maximal curvature in a quadratic Bézier curve is naturally the vertex of the parabola.
You can vary the parameter of the point , providing a rational quadratic Bézier curve, as in the Demonstration "Conic Section as Bézier Curve". See the details of that Demonstration for more information about rational Bézier curves.
A weight or produces an ellipse and a hyperbola, respectively.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+