Conjugate hyperbola

A hyperbola and its conjugate may be constructed as conic sections obtained from an intersecting plane that meets tangent double cones sharing the same apex.

Similarly, for a non-zero constant c, the coordinate axes form the asymptotes of the conjugate pair

Then ... the tangents form a parallelogram, and the diagonals of it, LM, L'M', pass through the center [C].

[2] In 1894 Alexander Macfarlane used an illustration of conjugate right hyperbolas in his study "Principles of elliptic and hyperbolic analysis".

[3] In 1895 W. H. Besant noted conjugate hyperbolas in his book on conic sections.

[4] George Salmon illustrated a conjugate hyperbola as a dotted curve in this Treatise on Conic Sections (1900).