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A straight line lying in the plane of a conic section (an ellipse, a hyperbola or a parabola, cf. Conic sections) and having the property that the ratio between the distance from any point on the curve to a focus of the curve and the distance from that point to the straight line is a constant magnitude, by definition equal to the eccentricity.


An ellipse and a hyperbola have both two foci and two associated directrices; a parabola has one focus and one directrix. Cf. also the comments to Focus of a curve.

How to Cite This Entry:
Directrix. E.V. Shikin (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098