Axes of Symmetry for Ellipse

Theorem

Let $K$ be an ellipse.

Then $K$ has exactly $2$ axes of symmetry:

the major axis of $K$

the minor axis of $K$.

Proof

From:

Major Axis of Ellipse is Axis of Symmetry

Minor Axis of Ellipse is Axis of Symmetry

we have that these diameters of $K$ are in fact axes of symmetry.

It remains to be shown that there are no more.

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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