A conic section directrix is the line that, together with a focus, defines the conic
section as the locus of points whose distance from
the focus is a fixed multiple of the perpendicular distance from the directrix. The constant
is the conic section's eccentricity. If , the curve 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.
of the perpendicular distance from the directrix. The constant
is the conic section's eccentricity. If 
, the curve is a parabola, if
,
it is an ellipse, and if 
, it is a hyperbola (Hilbert
and Cohn-Vossen 1999, p. 27).
