Eccentricity of Ellipse in terms of Semi-Major and Semi-Minor Axes

Theorem

Let $K$ be a ellipse such that:

$a$ denotes the length of the semi-major axis of $K$

$b$ denotes the length of the semi-minor axis of $K$

$e$ denotes the eccentricity of $K$.

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): ellipse
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): ellipse