directrix: meaning, definition, pronunciation and examples
C2Technical/Mathematical (Primary); Archaic/Historical (Secondary)
Quick answer
What does “directrix” mean?
A fixed line used to define and construct a parabola or other conic section.
Audio
Pronunciation
Definition
Meaning and Definition
A fixed line used to define and construct a parabola or other conic section.
A female director or manager; a woman who leads, guides, or supervises a group, organization, or activity. (This meaning is archaic/rare, with the mathematical definition being the primary modern sense.)
Dialectal Variation
British vs American Usage
Differences
No difference in core mathematical usage. The archaic personal sense is equally obsolete in both varieties.
Connotations
Purely technical/mathematical in modern use. No cultural or regional connotations.
Frequency
Exclusively encountered in advanced mathematics (geometry) contexts. Extremely low frequency in general language.
Grammar
How to Use “directrix” in a Sentence
[The] directrix of [a/the parabola/ellipse/hyperbola]distance from [point P] to [the] directrixVocabulary
Collocations
Usage
Meaning in Context
Business
Not used.
Academic
Used exclusively in advanced mathematics, specifically in geometry and analytic geometry contexts.
Everyday
Virtually never used.
Technical
The primary context. Essential for describing conic sections in mathematics, physics (orbital mechanics), and engineering.
Vocabulary
Synonyms of “directrix”
Neutral
Weak
Vocabulary
Antonyms of “directrix”
Watch out
Common Mistakes When Using “directrix”
- Using 'directrix' to mean a modern female director (use 'director' or 'woman director').
- Confusing 'directrix' (line) with 'focus' (point) when describing a parabola.
- Pronouncing it /daɪˈrɛktɹɪks/ (like 'director') instead of the standard /dɪˈrɛktrɪks/ or /daɪˈrɛktrɪks/.
FAQ
Frequently Asked Questions
No, this usage is archaic. The modern term for a female director is simply 'director'. The word 'directrix' is now almost exclusively a technical term in geometry.
They are the two key elements defining a conic section. For a parabola, the distance from any point on the curve to the focus is equal to its perpendicular distance to the directrix.
In British English, it is typically /dɪˈrɛktrɪks/ (di-REK-triks). In American English, both /daɪˈrɛktrɪks/ (dye-REK-triks) and /dɪˈrɛktrɪks/ are acceptable, with the first syllable often matching the vowel in 'direct'.
In standard definitions for conic sections (parabola, ellipse, hyperbola), each curve has a specific, single directrix associated with a given focus. However, an ellipse and hyperbola have two foci and two corresponding directrices.
A fixed line used to define and construct a parabola or other conic section.
Directrix is usually technical/mathematical (primary); archaic/historical (secondary) in register.
Learning
Memory Aids
Mnemonic
Think: To direct a parabola's path, it needs a FOCUS (point) and a DIRECTRIX (line). 'Directrix' contains 'direct' because it guides the shape.
Conceptual Metaphor
A GUIDING LINE (The directrix serves as a fixed rule or boundary that directs the formation of the curve).
Practice
Quiz
In which field is the term 'directrix' primarily used today?