Eccentricity of Hyperbola in terms of Semitransverse and Semiconjugate Axes

Theorem

Let $\KK$ be a hyperbola such that:

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

$b$ denotes the length of the semiconjugate axis of $\KK$

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

Then:

$e^2 = 1 + \dfrac {b^2} {a^2}$

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