# Definition:Hyperbola/Conjugate Axis

## Parts of Hyperbola

Consider a hyperbola $K$ whose foci are $F_1$ and $F_2$.

Let $PQ$ and $RS$ be line segments constructed through the vertices of $K$ parallel to the minor axis of $K$ and intersecting the asymptotes of $K$ at $P$, $Q$, $R$ and $S$ as above.

Construct the line segments $PR$ and $QS$.

Let $C_1$ and $C_2$ be the points of intersection of $PR$ and $QS$ with the minor axis of $K$.

The conjugate axis of $K$ is the line segment $C_1 C_2$.

## Also known as

Many sources give this as the minor axis, but at $\mathsf{Pr} \infty \mathsf{fWiki}$ the policy is to use the latter term to mean the (infinite) straight line which is the perpendicular bisector of the transverse axis of $K$.

## Linguistic Note

The plural of axis is axes, which is pronounced ax-eez not ax-iz.

Compare basis.