Apollonius theorem

The sum of the squares of the lengths of conjugate semi-diameters of an ellipse is constant and equal to the sum of the squares of the lengths of its semi-axes.

The area of a parallelogram circumscribed around an ellipse, with its sides oriented in opposite directions, is constant and equal to the product of the lengths of its diameters.

Comments

Cf. [a1] for a higher-dimensional generalization.

References

[a1]	K. Borsuk, "Analytic geometry" , PWN (1969)