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Directrix

Conic Sections The cui ves included in this group are obtained from plane sections of the cone. They include the circle, ehipse, parabola, hyperbola, and degeneratively the point and straight line. A conic is the locus of a point whose distance from a fixed point called the focus is in a constant ratio to its distance from a fixea line, called the directrix. This ratio is the eccentricity e. lie = 0, the conic is a circle if 0 < e < 1, the conic is an ellipse e = 1, the conic is a parabola ... [Pg.435]

Leit-linie, /. directrix, -rohr, n., -rohre, /. Leitungsrohr. -salz,n. conducting salt. -satz. [Pg.275]

A parabola is the set of points that are equidistant from a given fixed point (the focus) and from a given fixed line (the directrix) in the plane. The key-feature of a parabola is that it is quadrilateral in one of its coordinates and linear in the other. [Pg.53]

Figure 8.IB shows an experimental contour map of electron density for the H2O molecule in plane y-z, after Bader and Jones (1963). The electron density is higher around the nuclei and along the bond directrix. The experimental electron density map conforms quite well to the hybrid orbital model of Duncan and Pople (1953) with the LCAO approximation. Figure 8.IB shows an experimental contour map of electron density for the H2O molecule in plane y-z, after Bader and Jones (1963). The electron density is higher around the nuclei and along the bond directrix. The experimental electron density map conforms quite well to the hybrid orbital model of Duncan and Pople (1953) with the LCAO approximation.
A conic section or cotdc is the locus of a point which moves so that its distance from a fixed point (called the focus) is in a constant ratio (called the eccentricity) to the distance from a fixed straight line (called the directrix). [Pg.421]

Consider equation (7), 6.VIII N. Let the axes be turned through an angle in the negative direction so that OX coincides with ON and OY becomes parallel to the directrix ICH. Then =0,. . p=l and q=0, and the equation becomes ... [Pg.422]

The axis of a parabola is the line which passes through the focus and is perpendicular to the directrix. The vertex is the point where the axis crosses the parabola. The latus rectum is the chord passing through the focus and perpendicular to the axis. Its length is four times the distance from the focus to the vertex. [Pg.752]

This reflects the fact that all parabolas have the same eccentricity, namely 1. The eccentricity of a conic section is the ratio of the distances point-to-focus divided by point-to-directrix, which is the same for all the points on the conic section. Since, for a parabola, these two distances are always equal, their ratio is always 1. [Pg.752]

Directrix—The fixed line in the focus directrix definition of a conic section. [Pg.754]

The equations for conic sections can be expressed rather elegantly in polar coordinates. As shown in Fig. 5.9, the origin is defined as the focus and a line corresponding to x = d serves as the directrix. Recall the relations between the Cartesian and polar coordinates x = rcos 9, y = rsin6>. The point Fwill trace out the conic section, moving in such a way that the ratio of its distance to the focus r to its distance to the directrix d — x = d—rcos9 is a constant. This ratio is called the eccentricity, e (not to be confused with Euler s 6 = 2.718...) ... [Pg.82]

Ellipses and hyperbolas clearly have two distinct foci. The same ellipse or hyperbola can be constmcted using its other focus and a corresponding directrix. In terms of their semimajor and semiminor axes, the eccentricities of ellipses and hyperbolas are given by... [Pg.84]

A conic can be defined as a plane curve in which for all points on the curve the ratio of the distance from a fixed point (the focus) to the perpendicular distance from a straight line (the directrix) is a constant called the eccentricity e. For a parabola e = 1, for an ellipse e< 1, and for a hyperbola e> 1. [Pg.188]

Very frequently, the study of barrel arches can be referred to that of a unit depth arch, whose profile corresponds to the directrix curve of the vault. Therefore, barrel vaults can be reinforced by fabrics applied along the directrix, to both the lower or upper surfaces. For such reason, reinforcements are to be set at a spacing Pf, fulfilling the following inequality ... [Pg.108]

It is generally recommended to arrange along the generatrices an amount of reinforcement per unit area equal to 10 % of that arranged along the directrix. This percentage has to be increased up to 25 % in a seismic area. [Pg.108]

Cylindrical shells — shells in which either the directrix or the generatrix is a straight line. [Pg.201]

Think of a circle rolling on a straight line, thus a point S of the circle describes a cycloid consider, moreover, the cycloid traced by the mobile radius passing through the point S, and let P be the point of contact imagine finally, in a plane perpendicular to that of this cycloid, a parabola whose directrix is projected out of P, and which has S for its vertex this last curve, variable in size, will generate the surface. [Pg.100]


See other pages where Directrix is mentioned: [Pg.289]    [Pg.54]    [Pg.12]    [Pg.262]    [Pg.421]    [Pg.423]    [Pg.441]    [Pg.752]    [Pg.20]    [Pg.562]    [Pg.421]    [Pg.422]    [Pg.423]    [Pg.441]    [Pg.170]    [Pg.99]    [Pg.108]    [Pg.108]    [Pg.574]    [Pg.439]    [Pg.139]    [Pg.187]    [Pg.244]    [Pg.599]    [Pg.41]    [Pg.455]    [Pg.463]    [Pg.33]    [Pg.33]    [Pg.34]   
See also in sourсe #XX -- [ Pg.98 ]

See also in sourсe #XX -- [ Pg.82 ]




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Conic section directrix

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