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conic section: Quick Facts

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Facts

Also Known As conic

Photos

Diagram showing a double cone intersected by planes at different angles, producing the conic sections: a horizontal plane creates a circle, a tilted plane creates an ellipse, a plane parallel to the cone's side forms a parabola, and a steep plane produces a hyperbola. Each section is labeled, with the axis and apex of the cone indicated.
Eccentricity of conic sectionsThe eccentricity of a conic section completely characterizes its shape. For example, all circles have zero eccentricity, and all parabolas have unit eccentricity; hence, all circles (and all parabolas) have the same shape, only varying in size. (Under appropriate magnification they are indistinguishable.) In contrast, ellipses and hyperbolas vary greatly in shape.
Illustration showing how a parabolic satellite dish antenna focuses incoming transmission signals onto a single point, with red lines representing signal paths reflecting off the dish surface toward the feedhorn. Insets provide a side view and a three-quarter view, highlighting the role of the paraboloid shape in signal reception.
A diagram of a double cone intersected by two green planes labeled PP (picture plane) and RP (reality plane), illustrating projected conic sections in projective geometry, with the apex and a point Omega marked.
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Topics
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Key People

French philosopher Blaise Pascal
Blaise Pascal
French philosopher and scientist
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Apollonius of Perga
Greek mathematician
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Girard Desargues
French mathematician
Colin Maclaurin, engraving by S. Freeman; in the British Museum.
Colin Maclaurin
Scottish mathematician
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Conon of Samos
Greek mathematician
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Charles-Julien Brianchon
French mathematician
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Menaechmus
Greek mathematician

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