Eccentricity of Hyperbola is Interfocal Distance over Transverse Axis

Theorem

Let $\KK$ be a hyperbola such that:

$a$ denotes the length of the semitransverse axis of $\KK$

$c$ denotes the distance between the foci of $\KK$

$e$ denotes the eccentricity of $\KK$.

Then:

$e = \dfrac c {2 a}$

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): hyperbola
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): hyperbola