Definition:Hyperbola/Conjugate Axis

Parts of Hyperbola

 * ConjugateAxisOfHyperbola.png

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 the policy is to use the latter term to mean the (infinite) straight line which is the perpendicular bisector of the transverse axis of $K$.

Also see

 * Definition:Minor Axis of Hyperbola


 * Definition:Major Axis of Hyperbola
 * Definition:Transverse Axis of Hyperbola