conic section

Table of Contents

References & Edit History Quick Facts & Related Topics

Images

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.

Parabolic satellite dish antenna

Projective conic sectionsThe conic sections (ellipse, parabola, and hyperbola) can be generated by projecting the circle formed by the intersection of a cone with a plane (the reality plane, or RP) perpendicular to the cone's central axis. The image of the circle is projected onto a plane (the projective plane, or PP) that is oriented at the same angle as the cutting plane (Ω) passing through the apex (“eye”) of the double cone. In this example, the orientation of Ω produces an ellipse in PP.

For Students

conic section summary

Discover

Ahura Mazda - relief of the Zoroastrian god Ahura Mazda at the ancient ruins of Persepolis in Iran. Also known as Ormazd Zoroastrianism,

Which Religion Is the Oldest?

Panoramic view at sunrise of moai, Ahu Tongariki, Easter Island (Rapa Nui), Chile

6 Lost Civilizations

Dr. Martin Luther King Jr. addresses marchers during his "I Have a Dream" speech at the Lincoln Memorial in Washington. August 28th 1963

Was Martin Luther King, Jr., a Republican or a Democrat?

Black widow spider

9 of the World’s Deadliest Spiders

The Lost Colony of Roanoke, North Carolina, where 115 people mysteriously disappeared c. 1590. John White discovers the word Croatoan carved onto a tree upon his return to the deserted Roanoke Colony in 1590

The Lost Colony of Roanoke

International currencies, money, various banknotes, currency

A Brief (and Fascinating) History of Money

African Americans demonstrating for voting rights in front of the White House as police and others watch, March 12, 1965. One sign reads, "We demand the right to vote everywhere." Voting Rights Act, civil rights.

Timeline of the American Civil Rights Movement

conic section: Facts & Related Content

Written and fact-checked by The Information Architects of Encyclopaedia Britannica

Facts

Also Known As	conic

Photos

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.

Parabolic satellite dish antenna

Projective conic sectionsThe conic sections (ellipse, parabola, and hyperbola) can be generated by projecting the circle formed by the intersection of a cone with a plane (the reality plane, or RP) perpendicular to the cone's central axis. The image of the circle is projected onto a plane (the projective plane, or PP) that is oriented at the same angle as the cutting plane (Ω) passing through the apex (“eye”) of the double cone. In this example, the orientation of Ω produces an ellipse in PP.

See All Images →

Topics

latus rectum focus ellipse hyperbola parabola circle directrix eccentricity diameter radius involute catenary spiral Lissajous figure rhumb line brachistochrone curvature orthogonal trajectory tangent slope

Dig Deeper: More Articles That Discuss This Topic

projective geometry: Projective conic sections

Key People

Blaise Pascal

Blaise Pascal

French philosopher and scientist

Apollonius of Perga

Greek mathematician

Girard Desargues

French mathematician

Colin Maclaurin, engraving by S. Freeman; in the British Museum.

Colin Maclaurin

Scottish mathematician

Conon of Samos

Greek mathematician

Charles-Julien Brianchon

French mathematician

Menaechmus

Greek mathematician

Quiz

Equations written on blackboard

Numbers and Mathematics