Definition:Conjugate Diameters

Definition

Let $K$ be a conic section.

Let $D_1$ and $D_2$ be diameters of $K$ such that:

$D_1$ belongs to the system of parallel chords whose midpoints define $D_2$

and:

$D_2$ belongs to the system of parallel chords whose midpoints define $D_1$.

Then $D_1$ and $D_2$ are known as conjugate diameters.

Examples

Axes of Ellipse

The major axis and the minor axis of an ellipse are conjugate diameters.

Also see

• Results about conjugate Diameters can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): conjugate diameters
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): conjugate diameters