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The length of the conjugate axis is equal to 2b.
The conjugate axis or minor axis is perpendicular, or at a right angle to, the transverse axis.
Every hyperbola has a conjugate hyperbola, in which the transverse and conjugate axes are exchanged without changing the asymptotes.
Consider a line perpendicular to the transverse axis (i.e., parallel to the conjugate axis) that passes through one of the hyperbola's foci.
In his memoir on the theory of the conjugate axis and of the moment of inertia of bodies he enumerated the principle now known as Binet's theorem.
By symmetry a hyperbola has two directrices, which are parallel to the conjugate axis and are between it and the tangent to the hyperbola at a vertex.
The endpoints of the conjugate axis are at the height where a segment that intersects the vertex and is perpendicular to the transverse axis intersects the asymptotes.
The surface has two separate sheets when the axis of revolution is the transverse axis, but only one when the axis of revolution is the conjugate axis of the hyperbola.
A conjugate axis of length 2b, corresponding to the minor axis of an ellipse, is sometimes drawn on the non-transverse principal axis; its endpoints b lie on the minor axis at the height of the asymptotes over/under the hyperbola's vertices.
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