The directrix of a conic section is the line which, together with the point known as the focus, serves to define a conic section as the locus of points whose distance from the focus is proportional to the horizontal distance from the directrix, with being the constant of proportionality. If the ratio , the conic is a parabola, if , it is an ellipse, and if , it is a hyperbola (Hilbert and Cohn-Vossen 1999, p. 27).
Conic Section Directrix
See alsoConic Section, Ellipse, Focus, Hyperbola, Parabola
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ReferencesCoxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, pp. 115-116, 1969.Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 141-144, 1967.Eves, H. "The Focus-Directrix Property." §6.8 in A Survey of Geometry, rev. ed. Boston, MA: Allyn & Bacon, pp. 272-275, 1965.Hilbert, D. and Cohn-Vossen, S. "The Directrices of the Conics." Ch. 1, Appendix 2 in Geometry and the Imagination. New York: Chelsea, pp. 27-29, 1999.
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Weisstein, Eric W. "Conic Section Directrix." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ConicSectionDirectrix.html