directrices

directrices

A teacher draws the directrices of a parabola on the chalkboard.

Definition

  1. Noun (plural form of directrix):

    • In geometry: "directrices" are fixed lines used in the definition of a conic section (such as a parabola, ellipse, or hyperbola). The distance from a point on the conic to the focus is proportional to the distance from that point to the directrix.
    • In mathematics (general): A directrix is a line that, together with a focus, defines a curve or surface.

  2. Noun (rare, feminine form of director):

    • A female director: "directrices" can refer to women who direct or manage an organization, institution, or activity. This usage is uncommon and largely historical; the modern term "director" is gender-neutral.
Usage Examples

  • Geometry:

    • In a parabola, each point is equidistant from the focus and the directrix. (The directrix is a fixed line.)
    • The ellipse has two directrices, one associated with each focus. (The plural "directrices" refers to both lines.)

  • Rare usage (female director):

    • The directrices of the school oversaw the curriculum. (The female directors managed the school.)
Advanced Usage

  • "Directrices" in conic sections: In analytic geometry, the directrices are lines that help define the shape of a conic. For example, for an ellipse, the ratio of distances to the focus and directrix is constant (the eccentricity).

    • The eccentricity of a parabola is 1, meaning distances to focus and directrix are equal.

  • "Directrices" in calculus: In some contexts, "directrices" may appear in discussions of quadric surfaces, such as hyperboloids or paraboloids, where they serve as reference lines.

Variants and Related Words

  • Directrix (singular noun): the singular form of "directrices."

    • The directrix of a parabola is a fixed line. (A single line.)

  • Director (noun): a person who manages or guides, now used for all genders.

    • The director of the project approved the plan. (The manager.)

  • Directress (noun, feminine, rare): an alternative feminine form, similar to "directrix."

    • She served as directress of the charity. (The female leader.)
Synonyms
  • In geometry: guideline, reference line, fixed line.
  • In management: female director, manageress (dated), overseer (feminine).
Related Idioms
  • None common with "directrices" specifically, as it is a technical term.
Phrasal Verbs
  • None applicable; "directrices" is a noun and does not form phrasal verbs.