Two diameters y = m1x and y = m2x of $x^2$/$a^2$ - $y^2$/$b^2$ = 1 are conjugate if m1*m2 = $b^2$/$a^2$ (note: positive, unlike ellipse which has -$b^2$/$a^2$). Each conjugate diameter bisects chords parallel to the other. For the hyperbola, conjugate diameters cannot both intersect the same branch. The transverse and conjugate axes are the only pair of conjugate diameters that are perpendicular (only for rectangular hyperbola, all conjugate pairs are perpendicular).