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Topic: Conic section

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In the News (Wed 24 Apr 19)

  Conic Sections
Conic sections are among the oldest curves, and is an oldest math subject studied systematically and thoroughly.
The conics were first defined as the intersection of: a right circular cone of varying vertex angle; a plane perpendicular to an element of the cone.
The directrix of the conics is the intersection of the cutting plane and the plane of the tangent circle.
xahlee.org /SpecialPlaneCurves_dir/ConicSections_dir/conicSections.html   (1860 words)

 conic section
A conic section is an algebraic curve of the 2nd degree (and every 2nd degree equation represents a conic).
The conic section can be defined as the collection of points P for which the ratio 'distance to F / distance to l' is constant.
A conic section is used, together with a hexagon, to show Pascal's theorem (or its dual, Brianchon's theorem).
www.2dcurves.com /conicsection/conicsection.html   (403 words)

 Basic of Space Flight: Orbital Mechanics
A conic section, or just conic, is a curve formed by passing a plane through a right circular cone.
As shown in the figure to the right, the angular orientation of the plane relative to the cone determines whether the conic section is a circle, ellipse, parabola, or hyerbola.
The type of conic section is also related to the semi-major axis and the energy.
www.braeunig.us /space/orbmech.htm   (6457 words)

  Renkus-Heinz Inc. - Professional Loudspeakers
Their unique design is based on the spherical expansion of the acoustic pressure wave, so they don’t distort sound while controlling it, the way ordinary horns can.
The Complex Conic flare changes smoothly from a narrow diffraction slot, through an oval expansion, to a circular mouth.
Complex conic horns work better than ordinary horns, and they sound more natural too, with lower distortion an minimal coloration.
renkus-heinz.com /loudspeakers/sygma   (426 words)

  CONIC SECTION - Online Information article about CONIC SECTION
A conic may also be regarded as the polar reciprocal of a circle for a point;if the point be without the circle the conic is an ellipse, if on the circle a parabola, and if within the circle a hyperbola.
The conics are distinguished by the ratio between the latus rectum (which was originally called the latus erectum, and now often referred to as the parameter) and the segment of the ordinate intercepted between the diameter and the line joining the second vertex with the extremity of the latus rectum.
Wallis, in addition to translating the Conics of Apollonius, published in 1655 an original work entitled De sectionibus conicis nova methodo expositis, in which he treated the curves by the Cartesian method, and derived their properties from the definition in piano, completely ignoring the connexion between the conic sections and a cone.
encyclopedia.jrank.org /COM_COR/CONIC_SECTION.html   (3248 words)

  PlanetMath: conic section
The margin of the shadow of the ball is a conic, the ball is one of the Dandelin spheres of that conic, and the ball meets the table at the focus corresponding to that sphere.)
To work with conic sections in such an astronomical context, it is very useful to have a description in terms of polar coordinates centered at one focus.
Conic sections can be defined in a projective plane, even though, in such a plane, there is no notion of angle nor any notion of distance.
www.planetmath.org /encyclopedia/ConicSection.html   (818 words)

 PlanetMath: conic section
The margin of the shadow of the ball is a conic, the ball is one of the Dandelin spheres of that conic, and the ball meets the table at the focus corresponding to that sphere.)
To work with conic sections in such an astronomical context, it is very useful to have a description in terms of polar coordinates centered at one focus.
Conic sections can be defined in a projective plane, even though, in such a plane, there is no notion of angle nor any notion of distance.
planetmath.org /encyclopedia/ConicSection.html   (818 words)

 Conic Section Gallery
The following is a gallery of demos for illustrating selected families of conic sections These figures and animations can be used by instructors in a classroom setting or by students to aid in acquiring a visualization background relating to the change of parameters in expressions.
The conic sections are the non-degenerate curves generated by the intersections of a plane with one or two cones in the double cone as pictured below.
At http://math2.org/math/algebra/conics.htm is a discussion of conic sections generated by intersecting a double cone with detailed descriptions of the cases including degenerate cases.
mathdemos.gcsu.edu /mathdemos/family_of_functions/conic_gallery.html   (740 words)

 * Conic section - (Astronomy): Definition
Conic Section - One of four kinds of curves (circle, ellipse, hyperbola, and parabola) that can be formed by slicing a right circular cone with a plane...
A parabola is a conic section, a curve that is a set of points (P) such that the distance from a line (the directrix) to P is equal to the distance from P to focus F. Parabolas have an eccentricity of 1.
A hyperbola is a conic section (the intersection of a cone with a plane) that has two mirror-image branches.
en.mimi.hu /astronomy/conic_section.html   (299 words)

 Conic section - Definition, explanation
The conic sections were named and studied as long ago as 200 BC, when Apollonius of Perga undertook a systematic study of their properties.
The semi-latus rectum of a conic section, usually denoted l, is the distance from the single focus, or one of the two foci, to the conic section itself, measured along a line perpendicular to the major axis.
Conic sections are important in astronomy: the orbits of two massive objects that interact according to Newton's law of universal gravitation are conic sections if their common center of mass is considered to be at rest.
www.calsky.com /lexikon/en/txt/c/co/conic_section.php   (1303 words)

 Conic section Summary
A conic section is the plane curve formed by the intersection of a plane and a right-circular, two-napped cone.
The three conic sections are the parabola, hyperbola, and ellipse (the circle is considered a special case of an ellipse).
During this time the conic sections began to be defined as a locus of points in the plane rather than as sections of a plane intersecting a cone.
www.bookrags.com /Conic_section   (3862 words)

 Conic Sections - Search Results - MSN Encarta
Conic Sections, in geometry, two-dimensional curves produced by slicing a plane through a three-dimensional right circular conical surface.
Conic sections, a commonly studied topic of geometry, are two-dimensional curves created by slicing a plane through a three-dimensional hollow cone.
main article, circles as conic sections, conic projection, description, ellipses as conic sections, focus, hyperbolas as conic sections, parabolas...
encarta.msn.com /Conic_Sections.html   (150 words)

 [No title]   (Site not responding. Last check: )
The reduced equation of a conic section is the equation of a conic section translated and rotated so that its center lies in the center of the coordinate system and its axes are parallel to the coordinate axes.
If a plane intersects the cone when it is slanted the same as the side of the cone, (formally, when it is parallel to the slant height), the conic section is a parabola.
By using all of the conic section decks together, students become proficient at recognizing conic equation characteristics for circles, parabolas, ellipses and hyperbolas.
www.lycos.com /info/conic-section.html   (342 words)

 conic section - HighBeam Encyclopedia
conic section or conic, curve formed by the intersection of a plane and a right circular cone (conical surface).
The ordinary conic sections are the circle, the ellipse, the parabola, and the hyperbola.
When the plane passes through the vertex of the cone, the result is a point, a straight line, or a pair of intersecting straight lines; these are called degenerate conic sections.
www.encyclopedia.com /doc/1E1-conicsec.html   (255 words)

 News | TimesDaily.com | TimesDaily | Florence, AL   (Site not responding. Last check: )
In mathematics, a conic section (or just conic) is a curve that can be formed by intersecting a cone (more precisely, a right circular conical surface) with a plane.
If these points are real, the conic section must be a hyperbola, if they are imaginary conjugated, the conic section must be an ellipse, if the conic section has one double point at infinity it is a parabola.
If a conic section has one real and one imaginary point at infinity or it has two imaginary points that are not conjugated it is neither a parabola nor an ellipse nor a hyperbola.
www.timesdaily.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Conic_section   (1440 words)

 Chapter 8 Study Tips
Most of this chapter is devoted to the analytic geometry of conic sections, a topic which has diminished somewhat in emphasis since the introduction of so many other topics into the precalculus curriculum.
The opening discussion about general conic sections is simply to establish the correspondence between second-degree equations in two variables and sections of a double-napped right circular cone, a powerful connection indeed.
Graphs of rotated conic sections can be produced on regular graphers by following the procedure outlined in Example 3, but the effort required to split the equation into two functions leads most people to conclude that it is hardly worth it.
occawlonline.pearsoned.com /bookbind/pubbooks/demana_awl/chapter1/medialib/studytips/chapter8.html   (1438 words)

 Math In Nature - Conic Section   (Site not responding. Last check: )
A fascinating fact about the motions of all heavenly bodies (planets, comets, etc.) is that they all move in conic sections.
Conic sections are the ellipse, parabola, hyperbola, and the circle.
In fact all objects under the influence of gravity moves in conic sections.
library.thinkquest.org /23678/conic.html   (223 words)

 PlanetMath: tangent of conic section
The equation of the tangent line of an ordinary conic section (i.e., circle, ellipse, hyperbola and parabola) in the point
"tangent of conic section" is owned by pahio.
This is version 11 of tangent of conic section, born on 2004-07-16, modified 2005-01-31.
planetmath.org /encyclopedia/Polarize.html   (153 words)

 Analysis of conic sections
A conic section is the intersection of an extended cone and a plane.
Mathematically, conic sections are curves in a Cartesian plane described by second-degree equations in
To convert the general equation to a standard form, a rotation and a translation are applied to give a new set of coefficients for the equation the conic section that does not change its shape.
home.att.net /~srschmitt/conic_eqn_analysis.html   (1097 words)

 Advanced Math Software
Alg 2 / Pre Calculus
Trigonometry / Calculus Basics
This conic sections program begins by reviewing the procedure for "completing the square" — practice until proficient and then move on to find out what is a conic section.
The first of the conic sections to be studied is the circle followed by the parabola, the ellipse, and the hyperbola.
Learn the difference between conics whose center is the origin (0, 0) and conics whose center is not (h, k).
www.mathmedia.com /trigonometry.html   (1700 words)

 Multimedia: Conics
Move the slider for eccentricity and see what kind of conic section you get.
Move the focus to see what impact that has on the figure.
Move a point on the directrix to show that no matter what point is taken on the curve, the ratio of the distance to the focus over the distance to the directrix always equals the eccentricity.
www.brucesimmons.com /multimedia/multimedia_conics.htm   (62 words)

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