View source for 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. [[#References|[a1]]] for a higher-dimensional generalization.

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  K. Borsuk,   "Analytic geometry" , PWN  (1969)</TD></TR></table>