ellipse

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ellipse,

closed plane curve consisting of all points for which the sum of the distances between a point on the curve and two fixed points (foci) is the same. It is the conic sectionconic 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.
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 formed by a plane cutting all the elements of the cone in the same nappe. The center of an ellipse is the point halfway between its foci. The major axis is the chord that passes through the foci. The minor axis is the chord that passes through the center perpendicular to the major axis. The latus rectum is the chord through either focus perpendicular to the major axis. The vertices are the two points of intersection of the major axis with the curve. The eccentricity of an ellipse, a ratio of two lengths, is a measure of its flatness; it is the distance from the center to either focus divided by the distance from the center to either vertex. The circlecircle,
closed plane curve consisting of all points at a given distance from some fixed point, called the center. A circle is a conic section cut by a plane perpendicular to the axis of the cone.
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 may be considered an ellipse of eccentricity zero, i.e., one in which the center and the two foci all coincide.

ellipse

A closed curve that is a type of conic section with an eccentricity less than one. The longest line that can be drawn through the center of an ellipse is the major axis whereas the shortest line is the minor axis. The two axes are at right angles. There are two foci, which lie on the major axis and are symmetrically positioned on opposite sides of the center. The sum of the distances from the foci to a point moving round the ellipse is constant and equal to the length of the major axis. An orbiting body moves in an ellipse with the primary at one of the foci. See also Kepler's laws; orbit.

Ellipse

A closed loop obtained by cutting a right circular cone by a plane.

Ellipse

 

the intersection of a plane and one of the nappes of a circular conical surface (Figure 1).

Figure 1

An ellipse may also be defined as the locus of points M in the plane for which the sum of the distances from two fixed points F1 and F2 in the plane is constant; F1 and F2 are known as the foci of the ellipse. If a system of coordinates xOy is chosen as shown in Figure 2, then the equation of the ellipse assumes the form

Here, OF1 = OF2 = c, 2a = F1M + F2M, and Ellipse.

Figure 2

An ellipse is a quadratic curve. It is symmetric with respect to its axes AB and CD, and its center O is its center of symmetry. The line segments AB = 2a and CD = 2b are called the major and minor axes of the ellipse, respectively. The number e = cla < 1 is known as the eccentricity of the ellipse; if a = b, then e = 0 and the ellipse is a circle. The lines whose equations are x = –a/e and x = a/e are called the directrices of the ellipse; the ratio of the distance of a point of the ellipse from the nearest focus and the distance of the point from the nearest directrix is constant and equal to the eccentricity. The points A and B where the ellipse intersects its major axis are called its vertices. (See alsoCONIC SECTION.)

ellipse

[ə′lips]
(mathematics)
The locus of all points in the plane at which the sum of the distances from a fixed pair of points, the foci, is a given constant.

ellipse

a closed conic section shaped like a flattened circle and formed by an inclined plane that does not cut the base of the cone. Standard equation x2/a2 + y2/b2 = 1, where 2a and 2b are the lengths of the major and minor axes. Area: πab
References in periodicals archive ?
2] [desigual a] 0 se halla la ecuacion canonica de la elipse [kappa]-deformada
De forma general la calidad de un sistema de poligonacion estara dado en terminos de la incidencia que presenten las variables estadisticas de la medicion sobre las coordenadas; como producto de los errores accidentales en la medicion se obtienen las elipses absolutas de error que determinan la incertidumbre en el posicionamiento de cada vertice, las elipses relativas que dan cuenta de la precision que existe entre un par de estaciones, su orientacion esta definida por el angulo que se forma entre el semieje mayor y la linea que une la estacion con el punto a observar.
El angulo [sigma] se corresponde con el angulo de orientacion de la elipse respecto del eje longitudinal, fijado en 120[grados].
El sentido que brinda la figura de elipse no tiene que ver tanto con la duplicacion de su centro, como con la tension y movimiento que se instala en aquel centro a partir de esa duplicacion, y que termina con la posibilidad de la quietud que ofrece lo unitario.
La actitud paternalista de Kopp en las relaciones laborales a los albores de la industrializacion colombiana (15) lo transfiguro, en la vida diaria de la elipse, en una suerte de "patron de los desempleados", que hasta el dia de hoy hacen cola para susurrarle sus plegarias al oido de su escultura en bronce, cuya postura recuerda el pensador de Rodin.
Luane's first Louis Vuitton bag is an Elipse Monogram piece.
Other moves worth mentioning included AU Insurance's acquisition of first-floor accommodation at CP1, Crucible Park (15,000 sq ft) following their relocation from the nearby Axis Court and Admiral Insurance, which has expanded again at SA1 by taking a further 6,000 sq ft at the Elipse Building at a headline rent of PS14.
La circunferencia y la elipse son funciones que al cruzarse y ser rotadas en el eje x, generan volumenes similares al menisco ocular observado en la pantalla del ecografo (8).
Con el monitor BIVA se considero que el estado de hidratacion era adecuado cuando el vector de impedancia se mantiene en el eje de hidratacion dentro de la elipse de tolerancia del 75% tanto en los controles pre como postdialisis (16).
Entre el gran exterior una falda de colores se elevaba desde un segmento de la figura hasta un punto mas alla de la cuadricula, y por encima de ella una mas que la seguia en su orbita, pero cuyo final se ocultaba tras la media elipse de la inferior.