Hyperbola

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

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1. **Definition**: A hyperbola is the locus where the absolute difference of distances from two foci is constant.
2. **Expansion**: The standard horizontal hyperbola equation is $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$.
3. **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.
4. **Asymptotes**: The lines $y = \pm (b/a)x$ serve as asymptotes.

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