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# Conic Section Directrix

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).

Hyperbolas and noncircular ellipses have two distinct foci and two associated directrices, each directrix being perpendicular to the line joining the two foci (Eves 1965, p. 275).

Conic Section, Ellipse, Focus, Hyperbola, Parabola

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## References

Coxeter, 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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Conic Section Directrix

## Cite this as:

Weisstein, Eric W. "Conic Section Directrix." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ConicSectionDirectrix.html