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).
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.
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).
