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).
See also
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." ยง6.8 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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Cite this as:
Weisstein, Eric W. "Conic Section Directrix." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ConicSectionDirectrix.html