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- {{Short description|Conic sections with the same foci}} In [[geometry]], two [[conic section]]s are called '''confocal''' if they have the same [[Focus (geometr ...22 KB (3,462 words) - 03:29, 20 January 2025
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- {{short description|Relation between conic sections and triangles}} ...c.svg|thumb|upright=1.0|6 points on the sides of triangle and their common conic section]] ...1 KB (225 words) - 21:51, 14 May 2022
- {{short description|Collinearity of the midpoints of parallel chords in a conic}} ...onic section|conic]]. It states that the midpoints of parallel chords in a conic are located on a common line. ...2 KB (275 words) - 06:58, 4 April 2024
- A hyperbola and its conjugate may be constructed as [[conic section]]s obtained from an intersecting plane that meets tangent double co ...classicist)|Thomas Heath]] (1896) ''Apollonius of Perga: Treatise on Conic Sections'', pages 47, 48, 54</ref> "The two hyperbolas so constructed are called ''' ...6 KB (872 words) - 01:04, 27 February 2025
- ...c object from data concerning its projections (shadows) on planes or cross-sections by planes."<ref name="ref1"> *[[Generalized conic]] ...2 KB (202 words) - 02:45, 19 July 2023
- {{Short description|Unique point and line of a conic section}} ...line that have a unique reciprocal relationship with respect to a given [[conic section]]. ...12 KB (1,946 words) - 21:36, 7 January 2025
- {{Short description|Pairs of conic sections in geometry}} One should not mix focal conics with [[Confocal conic sections|confocal conics]]. The latter ones have all the same foci. ...5 KB (715 words) - 03:28, 20 January 2025
- ...e:Steiner-erz-def-s.svg|thumb|1. Definition of the Steiner generation of a conic section]] ...thod to define a non-degenerate [[Quadric (projective geometry)|projective conic section]] in a [[projective plane]] over a [[Field (mathematics)|field]]. ...14 KB (2,285 words) - 05:43, 3 May 2024
- In [[geometry]], two [[diameter]]s of a [[conic section]] are said to be '''conjugate''' if each [[chord (geometry)|chord]] ...classicist)|Thomas Heath]] (1896) ''Apollonius of Perga: Treatise on Conic Sections'', page 64</ref> ...8 KB (1,181 words) - 03:19, 29 December 2024
- ...ola]] the director circle degenerates to a straight line, the [[Directrix (conic section)|directrix]] of the parabola.<ref>{{harvnb|Faulkner|1952|page=83}}< | title = Some new ratios of conic curves ...4 KB (545 words) - 06:02, 8 July 2024
- ...]]'' [[projective plane]] of ''odd'' order is a nondegenerate projective [[conic section]]. ...one tangent. The standard examples are the nondegenerate projective conic sections. ...10 KB (1,641 words) - 03:30, 23 August 2023
- ...e [[Pole and polar|polar]] of point P with respect to (S) or D lies on the conic (S). Let DA' ∩ BC =A<sub>0</sub>; DB' ∩ AC = B<sub>0</sub>; DC' ∩ AB= C<sub [[Category:Conic sections]] ...6 KB (919 words) - 02:25, 9 August 2021
- ...line]] (a degree-1 [[plane curve]]). There are additional subtleties for [[conic]]s that do not exist for lines, and thus the statement and its proof for co ...ible, because it contains a line), and may not be unique; see [[Degenerate conic#Points to define|further discussion]]. ...15 KB (2,250 words) - 03:28, 23 September 2023
- == Translation of conic sections == {{Main|Conic section}} ...9 KB (1,417 words) - 18:06, 15 October 2024
- ...the first to use [[Analytic geometry|Cartesian]] methods to study [[conic sections]].<ref>{{Cite book|url=https://books.google.com/books?id=owEj9TMYo7IC&dq=Jo ...2 KB (233 words) - 05:29, 7 September 2024
- [[Category:Conic sections]] ...2 KB (273 words) - 06:13, 13 March 2024
- ...rthogonal trajectories]]. Special examples are systems of [[confocal conic sections]]. The article [[confocal conic sections]] deals with confocal ''quadrics'', too. They are a prominent example of a ...11 KB (1,679 words) - 19:52, 13 July 2023
- *[[Generalized conic]] [[Category:Conic sections]] ...4 KB (585 words) - 05:44, 11 April 2023
- ...\mathcal P,\mathcal Z, \in) </math> is isomorphic to the geometry of plane sections of a circular cylinder in <math>\R^3</math> . ...hat <math>\mathcal L(K) </math> is isomorphic to the geometry of the plane sections on a quadric cylinder over field <math> K </math>. ...12 KB (2,021 words) - 00:08, 6 August 2024
- The above polar equation describes [[conic section]]s, with <math>l</math> the [[semi-latus rectum]] (equal to <math>h ...uces a noncircular [[elliptical orbit]] (or more generally a noncircular [[conic section]]) around a [[focus (geometry)|focus of the ellipse]]? ...9 KB (1,390 words) - 18:45, 22 May 2024
- {{distinguish|Steiner conic}} ...enter of the ellipse. This is true for the circumcircle. A [[Conic section|conic]] is uniquely determined by 5 points. Hence the circumcircle is the only St ...10 KB (1,585 words) - 20:05, 4 February 2025