“parabola”的概念、定义、翻译、参考文献-科学参考

parabola

Physics

A conic with eccentricity e=1. It is the locus of a point that moves so that its distance from the focus is equal to its perpendicular distance from the directrix. A chord through the focus, perpendicular to the axis, is called the latus rectum. For a parabola with its vertex at the origin, lying symmetrically about the x-axis, the equation is y²=4ax, where a is the distance from the vertex to the focus. The directrix is the line x=−a, and the latus rectum is 4a.

Parabola.

Mathematics

A conic with eccentricity equal to 1. Thus a parabola is the locus of all points P such that the distance from P to a fixed point F (the focus) is equal to the distance from P to a fixed line l (the directrix). It is obtained as a plane section of a cone in the case when the plane is parallel to a generator of the cone (see conic). A line through the focus perpendicular to the directrix is the axis of the parabola, and the point where the axis cuts the parabola is the vertex. It is possible to take the vertex as origin, the axis of the parabola as the x-axis and the focus as the point (a,0). In this coordinate system, the directrix has equation x =−a and the parabola has equation y² =4ax (see normal form of conics).

A parabola with focus and directrix

Different values of a give parabolas of different sizes, but all parabolas are the same shape (i.e. are similar to one another). The equations x = at², y = 2at are parametric equations for the parabola y² = 4ax.

For a point P on the parabola, let α‎ be the angle between the tangent at P and a line through P parallel to the axis of the parabola, and let β‎ be the angle between the tangent at P and a line through P and the focus, as shown in the figure below;

A parabolic reflector

then α‎ = β‎. This is the basis of the parabolic reflector: if a source of light is placed at the focus of a parabolic reflector, each ray of light is reflected parallel to the axis, so producing a parallel beam of light.
http://www.calculus.org/Contributions/animations.html Properties of the parabola with links to animated illustrations.

Astronomy

A type of curve whose ‘arms’ become parallel as they approach infinity, so that the curve never quite closes in on itself, defined mathematically as a conic section with an eccentricity of 1. It may be regarded as an ellipse in which the two foci are infinitely far apart, and is the limiting case between an ellipse and a hyperbola. Some comets have elliptical orbits that are so extended they are indistinguishable from parabolas.

单词	parabola
释义	parabola Physics A conic with eccentricity e=1. It is the locus of a point that moves so that its distance from the focus is equal to its perpendicular distance from the directrix. A chord through the focus, perpendicular to the axis, is called the latus rectum. For a parabola with its vertex at the origin, lying symmetrically about the x-axis, the equation is y²=4ax, where a is the distance from the vertex to the focus. The directrix is the line x=−a, and the latus rectum is 4a. Parabola. Mathematics A conic with eccentricity equal to 1. Thus a parabola is the locus of all points P such that the distance from P to a fixed point F (the focus) is equal to the distance from P to a fixed line l (the directrix). It is obtained as a plane section of a cone in the case when the plane is parallel to a generator of the cone (see conic). A line through the focus perpendicular to the directrix is the axis of the parabola, and the point where the axis cuts the parabola is the vertex. It is possible to take the vertex as origin, the axis of the parabola as the x-axis and the focus as the point (a,0). In this coordinate system, the directrix has equation x =−a and the parabola has equation y² =4ax (see normal form of conics). A parabola with focus and directrix Different values of a give parabolas of different sizes, but all parabolas are the same shape (i.e. are similar to one another). The equations x = at², y = 2at are parametric equations for the parabola y² = 4ax. For a point P on the parabola, let α‎ be the angle between the tangent at P and a line through P parallel to the axis of the parabola, and let β‎ be the angle between the tangent at P and a line through P and the focus, as shown in the figure below; A parabolic reflector then α‎ = β‎. This is the basis of the parabolic reflector: if a source of light is placed at the focus of a parabolic reflector, each ray of light is reflected parallel to the axis, so producing a parallel beam of light. http://www.calculus.org/Contributions/animations.html Properties of the parabola with links to animated illustrations. Astronomy A type of curve whose ‘arms’ become parallel as they approach infinity, so that the curve never quite closes in on itself, defined mathematically as a conic section with an eccentricity of 1. It may be regarded as an ellipse in which the two foci are infinitely far apart, and is the limiting case between an ellipse and a hyperbola. Some comets have elliptical orbits that are so extended they are indistinguishable from parabolas.
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