Conic Sections

Irina Boyadzhiev, Radek Novak, Sep 16, 2018

A collection of several 2D and 3D GeoGebra applets for studying the conics (ellipse, parabola, and hyperbola)


  • 1. Conic Sections
  • 2. On the geometric definition of ellipse
  • 3. How to construct a hyperbola
  • 4. How to construct a parabola
  • 5. Conic Section - A Geometric Construction using Eccentricity
  • 6. Dandelin Spheres
  • 7. Reflective Properties of the Conics
  • 8. Locus of the centers of all circles tangent to two circles
  • 9. Some fascinating properties of the conic sections

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Conic Sections

A conic section is the intersection of a plane and a cone. The three conic sections ellipse, parabola or hyperbola can be produced by changing the slope of the plane (that is, the angle between the axes of the cone and the intersecting plane).[br]In the applet below we consider an infinite cone with an angle [math]\alpha[/math].[br][*]Play the animation to see a demonstration of the conics, hyperbola, parabola, ellipse and circle.[br][*]Stop the animation and explore additional special cases by changing the angle of the plane (drag the orange point) and the location of the plane (drag the brown point).
– Irina Boyadzhiev

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