This page is a sub-page of our page on Plane Curves.
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Related KMR-pages:
• Optical properties of Conics
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Other related sources of information:
• Appolonius of Perga
• Diocles
• Ellipse
• The vertices of an ellipse
• Ellipse as a Hypotrochoid
• Parabola
• Hyperbola
• Conic Section
• Dynamic construction of the ellipse and other curves
• Proof that the directrix-focus and the focus-focus definitions are equivalent
• How was the focus/directrix property of conic sections discovered?
• Dandelin’s construction (in Spanish)
• Lemniscate-Of-Bernoulli
• Ever wondered why slicing a cone gives an ellipse? It’s wonderfully clever!
• Midpoint tracing of a Parabola at geogebra.org
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The interactive simulations on this page can be navigated with the Free Viewer
of the Graphing Calculator.
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Drawing ellipses (Pavel Boytchev on YouTube):
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Ellipse – counterrotate:
The interactive simulation that created this movie.
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Drawing hyperbolas (by Pavel Boytchev):
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The Ellipse, the Parabola, and the Hyperbola and their properties
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The interactive simulation that created this movie.
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Dandelin’s construction – Fixed elliptical crossection and moving sphere:
The interactive simulation that created this movie.
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Dandelin’s construction – Moving parabolic crossection and tangential sphere:
The interactive simulation that created this movie.
NOTE: The Dandelin sphere touches the plane of the parabola at the focus of the latter.
The (grey) plane through the horizontal (yellow) circle intersects the (light-blue) plane of the parabola in its (red) directrix.
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Dandelin Spheres (Gian Marco Todesco on YouTube):
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Dandelins Spheres (Nicholas Stafford and Carlos Fernandez on YouTube):
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Hyperbolas in the real world (TXbasketball35 on YouTube):
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From Ellipse to Hyperbola (Thaddeus Wert on YouTube):
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A link to the page on Optical properties of conics
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Inverse curves involving conics
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The interactive simulation that created this movie.
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Hyperbola-centre-Inverse curves:
The interactive simulation that created this movie.
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The interactive simulation that created this movie.
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The interactive simulation that created this movie.
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The interactive simulation that created this movie.
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Hyperbola-vertex-inverse:
The interactive simulation that created this movie.
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Sinusoidal Spirals at Wikipedia
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Lemniscate-Of-Bernoulli-center-inverse:
The interactive simulation that created this movie.
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