rectangular hyperbola: meaning, definition, pronunciation and examples
C2 (Proficiency)Technical/Specialized
Quick answer
What does “rectangular hyperbola” mean?
A hyperbola whose asymptotes are perpendicular to each other. In its simplest form, it is represented by the equation xy = c, where c is a constant.
Audio
Pronunciation
Definition
Meaning and Definition
A hyperbola whose asymptotes are perpendicular to each other. In its simplest form, it is represented by the equation xy = c, where c is a constant.
In analytic geometry, a hyperbola for which the angle between the asymptotes is 90°, equivalent to one with eccentricity √2. The term is also used in various applied mathematics contexts, such as describing certain inverse relationships in economics or physics.
Dialectal Variation
British vs American Usage
Differences
No significant differences in mathematical definition or usage. Minor potential variation in the frequency of the synonymous term 'equilateral hyperbola'.
Connotations
Purely technical, with no cultural connotations.
Frequency
Extremely low frequency in general language, confined to advanced mathematics, physics, and engineering texts.
Grammar
How to Use “rectangular hyperbola” in a Sentence
The [curve/graph] is a rectangular hyperbola.Plot the rectangular hyperbola defined by xy = [constant].The relationship is described by a rectangular hyperbola.Vocabulary
Collocations
Examples
Examples of “rectangular hyperbola” in a Sentence
adjective
British English
- The rectangular-hyperbola solution was the most elegant.
- They derived a rectangular-hyperbola relationship from the data.
American English
- The rectangular-hyperbola solution was the most elegant.
- They derived a rectangular-hyperbola relationship from the data.
Usage
Meaning in Context
Business
Virtually never used.
Academic
Used in advanced mathematics, physics (e.g., Boyle's Law graph), and engineering courses and literature.
Everyday
Never used.
Technical
The primary context of use. Found in technical papers, textbooks, and problem sets involving conic sections or inverse proportionality.
Vocabulary
Synonyms of “rectangular hyperbola”
Neutral
Watch out
Common Mistakes When Using “rectangular hyperbola”
- Confusing it with a rectangular *shape* or a parabola.
- Misspelling as 'rectangler hyperbola' or 'hyperbole'.
- Misidentifying the graph of y = 1/x as something other than a rectangular hyperbola.
FAQ
Frequently Asked Questions
Yes, the graph of y = 1/x (or xy = 1) is the canonical example of a rectangular hyperbola centred at the origin.
The eccentricity (e) of a rectangular hyperbola is √2.
Yes, in standard analytic geometry, the terms are synonymous, both describing a hyperbola with perpendicular asymptotes.
Classic examples include the graph of Boyle's Law in physics (pressure vs. volume of an ideal gas at constant temperature) and certain economic models showing inverse relationships, like some demand curves with unit elasticity.
A hyperbola whose asymptotes are perpendicular to each other. In its simplest form, it is represented by the equation xy = c, where c is a constant.
Rectangular hyperbola is usually technical/specialized in register.
Rectangular hyperbola: in British English it is pronounced /rɛkˈtæŋɡjʊlə haɪˈpɜːbələ/, and in American English it is pronounced /rɛkˈtæŋɡjələr haɪˈpɜːrbələ/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think: A hyperbola whose arms are boxed in by perpendicular (like the corners of a rectangle) guide-lines (asymptotes). 'Rect-' for right angles, 'hyperbola' for the curve.
Conceptual Metaphor
None in common usage.
Practice
Quiz
What is the defining geometric property of a rectangular hyperbola?