Hyperbola

Easymathematics

The standard equation of a hyperbola with transverse axis along x-axis is

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x²/a² - y²/b² = 1

x²/a² + y²/b² = 1

y²/a² - x²/b² = 1

x² - y² = a²

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Subject: mathematics
Chapter: coordinate geometry
Topic: hyperbola
Difficulty: Easy
Year: 2025

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x²/a² - y²/b² = 1

Definition: A hyperbola is the locus where the absolute difference of distances from two foci is constant.
Expansion: The standard horizontal hyperbola equation is $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ .
Interpretation: The minus sign distinguishes it from the ellipse. The positive term ( $x^{2}$ ) indicates that the transverse axis (the one passing through the vertices) is the x-axis.
Asymptotes: The lines $y = \pm (b / a) x$ serve as asymptotes.

This easy difficulty mathematics question is from the chapter coordinate geometry, covering the topic of hyperbola. It appeared in the 2025 exam.

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Hyperbola

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