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 $K$.
Also see
Linguistic Note
The plural of axis is axes, which is pronounced ax-eez not ax-iz.
Compare basis.
Sources
- 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text {V}$. The Hyperbola: $2$.
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): conjugate axis
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): hyperbola