Hyperbola

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The eccentricity of a hyperbola is always

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1. **Relationship**: For a hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, the semi-minor and semi-major axes relate to eccentricity as $b^2 = a^2(e^2 - 1)$.
2. **Constraint Analysis**: Since $b^2$ and $a^2$ are both positive, $e^2 - 1$ must be positive.
3. **Result**: $e^2 > 1 \implies **e > 1**$.
- This reflects that the distance from the center to a focus ($ae$) is greater than the distance to the vertex ($a$).

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