directrix

directrix

A parabola is defined by its focus and directrix.

Definition
  1. Noun:
    • Geometry: A fixed line used in the definition of a conic section (such as a parabola, ellipse, or hyperbola). For a given point (the focus) and a given line (the directrix), the conic section is the set of all points whose distance to the focus is proportional to its perpendicular distance to the directrix.
    • Archaic: A female director, guide, or ruler (synonymous with "directress").
Usage Examples

  • Geometry:

    • In a parabola, each point is equidistant from the focus and the directrix. (The fixed line serves as a geometric reference for the curve.)
    • The directrix of an ellipse is a line perpendicular to the major axis. (The fixed line defines the shape of the ellipse.)

  • Archaic:

    • She acted as the directrix of the charitable foundation. (She served as a female director or leader.)
Advanced Usage

  • "Directrix of a parabola": The fixed line used in the geometric definition of a parabola.

    • To construct a parabola, you need a focus point and a directrix line. (The directrix is essential for plotting the curve.)

  • "Directrix of a conic": In advanced geometry, the directrix is part of the definition for all conic sections, not just parabolas.

    • Each conic section has a focus and a corresponding directrix. (The directrix determines the eccentricity of the shape.)
Variants and Related Words

  • Directress (n): a female director or manager (archaic synonym).

    • The directress of the school was highly respected. (The female head of the school.)

  • Directorial (adj): relating to a director or direction.

    • The directorial decisions shaped the project. (Decisions made by the director.)
Synonyms
  • Guide: something that directs or indicates a course.
    • The directrix acts as a guide for the curve. (The line directs the shape.)
  • Ruler: a straight line used for measurement or guidance (geometric sense).
    • The directrix functions as a ruler for the conic. (A fixed line of reference.)
Related Idioms
  • Follow the directrix: (uncommon) to adhere strictly to a guiding principle or rule.
    • In her career, she always followed the directrix of ethical conduct. (She adhered to a guiding standard.)
Phrasal Verbs
Related Idioms
  • By the directrix: (rare) referring to a method based on a fixed standard.
    • The design was created by the directrix of symmetry. (Following a fixed geometric line.)