Conics

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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Conic Sections:

The interactive simulation that created this movie.

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Dandelin’s construction

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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Ellipse-centre-inverse:

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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Ellipse-focus-inverse:

The interactive simulation that created this movie.

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Hyperbola-focus-inverse:

The interactive simulation that created this movie.

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Ellipse-vertex-inverse:

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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