Conic sections
The four classic conic sections: circle (red), ellipse (green), parabola (blue) and hyperbola (yellow).
Conic Sections :
Any curve produced by the intersection of a plane and a right circular cone. Depending on the angle of the plane relative to the cone, the intersection is a circle, an ellipse, a hyperbola, or a parabola.
conic section: any of the range of geometric curves produced by the intersection of plane with a cone (i.e. circles, ellipses, parabolas and hyperbolas). The first detailed study was by Apollonius.
contingent line: see tangent line.
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 ...
Conic Sections -- The family of curves generated by planes intersecting with a cone. Several cases are distinguished, depending on the angle between the plane and the axis of the cone.
Five coaxial conic sections can form an X-ray image.
[A] True
[B] False
The first target of observation by an imaging X-ray system was: ...
Conic Sections
The right line drawn through the two points of contact of the two tangents drawn from a given point to a given conic section. The given point is called the pole of the line.
See conic section. The limiting case occurs when the point is on the line, in which case the parabola becomes a straight line. parabolic Pertaining to, or shaped like, a parabola.
Originally called conic section.
The conic sections are the ellipse, the parabola, and the hyperbola, curves that are used to describe the path or bodies moving in space.
He understood the parabola, both in terms of conic sections and in terms of the ordinate (y) varying as the square of the abscissa (x).
With two bodies, an orbit is a conic section. The orbit can be open (so the object never returns) or closed (returning), depending on the total kinetic + potential energy of the system.
Euclid also wrote works on perspective, conic sections, spherical geometry, and possibly quadric surfaces. Neither the year nor place of his birth have been established, nor the circumstances of his death.
The Elements ...
In the absence of planetary perturbations and nongravitational forces, a comet will orbit the Sun on a trajectory that is a conic section with the Sun at one focus.
In astrodynamics, under standard assumptions in astrodynamics, any orbit must be of conic section shape. The eccentricity of this conic section, the orbit's eccentricity, is an important parameter of the orbit that defines its absolute shape....
Conic Sections and Gravitational Orbits
The ellipse is not the only possible orbit in a gravitational field.
Newton's gravitational theory also predicts that in general, the orbit of an object can be any of the four conic sections: circle, ellipse, parabola and hyperbola; as well as the straight line.
The meteors, whatever their dimensions, must have motions around the sun in obedience to the law of gravitation in the same manner as planets and comets - that is, in conic sections of which the sun is always at one focus.
PARABOLA
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.
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HYPERBOLA
A hyperbola is a conic section (the intersection of a cone with a plane) that has two mirror-image branches. Hyperbolas have an eccentricity greater than 1.
HYPERBOLIC ORBIT
A hyperbolic orbit is an in which the is greater than 1.
A number used in optics to specify the shape of a surface which is a conic section, i.e. parabolic, hyperbolic, elliptical. Conic sections are obtained by slicing through a cone at the appropriate angle. [McL97]
Conifold Transition ...
Hypatia wrote commentaries on the astronomical canon of Ptolemy and did work on conic sections . Her works are lost, but are referred to in the Suda lexicon.
Follow this link for a more thorough treatment of conic sections, leading to orbital mechanics.
SKIP QUIZ ...
2D computer graphics
Brahmagupta's formula
Complex geometry
Conic section ...
In his Principia Mathematica of 1687, Isaac Newton proved that an object moving under the influence of his inverse square law of universal gravitation must trace out an orbit shaped like one of the conic sections, ...
 See also: Distance, Orbit, Sun, Earth, Circle
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