The Jerabek hyperbola is a circumconic that is the isogonal conjugate of the Euler line (Kimberling 1998, p. 237). Since it is a circumconic passing through the orthocenter, it is a rectangular hyperbola and has center on the nine-point circle. Its circumconic parameters are given by
![x:y:z=a[sin(2B)-sin(2C)]:b[sin(2C)-sin(2A)]:c[sin(2A)-sin(2B)],](/images/equations/JerabekHyperbola/NumberedEquation1.svg) |
(1)
|
meaning it has trilinear equation
![(a[sin(2B)-sin(2C)])/alpha+(b[sin(2C)-sin(2A)])/beta+(c[sin(2A)-sin(2B)])/gamma=0,](/images/equations/JerabekHyperbola/NumberedEquation2.svg) |
(2)
|
or equivalently
 |
(3)
|
(P. Moses, pers. comm., Apr. 19, 2005), where 
, 
, and 
are Conway triangle
notation.
It passes through the vertices of a triangle as well as Kimberling centers 
for 
(circumcenter), 4 (orthocenter),
6 (symmedian point), 54 (Kosnita
point), 64 isogonal conjugate of the de Longchamps point), 65 (orthocenter
of the contact triangle), 66 (isogonal
conjugate of the Exeter point), 67 (isogonal
conjugate of the far-out point), 68 (Prasolov
point), 69, 70, 71, 72, 73, 74, 248, 265, 290, 695, 879, 895, 1173, 1175, 1176,
1177, 1242, 1243, 1244, 1245, 1246, 1439, 1798, 1903, 1942, 1987, 2213, 2435, 2574,
2575, 2992, and 2993.
The Jerabek center is Kimberling center 
,
which has equivalent triangle center functions
 |  |  |
(4)
|
 |  |  |
(5)
|
 |  |  |
(6)
|
(Kimberling 1998, p. 87).
