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Trigonometry and geometry
Published in C.W. Evans, Engineering Mathematics, 2019
We consider a fixed straight line called the directrix and a fixed point S called the focus (Fig. 3.19). If P is a general point, suppose L is a point on the directrix such that the line PL and the directrix are perpendicular to one another. If the ratio PS/PL is a constant then the locus of P is one of the conic sections. The ratio e = PS/PL is known as the eccentricity. We consider the three cases e = 1, e < 1 and e > 1.
Analytic Geometry
Published in Richard C. Dorf, Ronald J. Tallarida, Pocket Book of Electrical Engineering Formulas, 2018
Richard C. Dorf, Ronald J. Tallarida
A parabola is the set of all points (x, y) in the plane that are equidistant from a given line called the directrix and a given point called the focus. The parabola is symmetric about a line that contains the focus and is perpendicular to the directrix. The line of symmetry intersects the parabola at its vertex (Figure 4.4). The eccentricity e = 1.
Methods of Spatial Visualisation
Published in Ken Morling, Stéphane Danjou, Geometric and Engineering Drawing, 2022
A parabola is the locus of a point that moves so that its distance from a fixed point (called the focus) bears a constant ratio of 1 to its perpendicular distance from a straight line (called the directrix).
Non-equivalent notions of the eccentricity of the conics: an exploratory study with high school teachers
Published in International Journal of Mathematical Education in Science and Technology, 2023
Antonio Rivera-Figueroa, Ernesto Bravo-Díaz
It is a second approach, where the conics are also conceived as loci (plural of locus), but now the three curves, parabola, ellipse, and hyperbola, are defined in terms of one focus and a directrix; in this definition, the circle is not considered. A conic is the locus of the points P of a plane, such that the ratio of the distance of P from a fixed point F, called focus, to the distance of P from a fixed line l, called directrix, which does not contain F, is a positive constant e. This constant is defined as the eccentricity of the conic (see, e.g. Apostol, 1966, p. 500; Edwards & Penney, 1994, pp. 536–537; Leithold, 1981, p. 679; Rider, 1947, p. 142; Simmons, 1996, p. 552). The curve is a parabola when ; it is an ellipse when and a hyperbola when . (Figure 2)