From The Collaborative International Dictionary of English v.0.48 [gcide]:
Conjugate \Con"ju*gate\, adjective [L. conjugatus, p. p. or conjugare to unite; con- + jugare to join, yoke, marry, jugum yoke; akin to jungere to join. See {Join}.]
1. United in pairs; yoked together; coupled.
2. (Bot.) In single pairs; coupled.
3. (Chem.) Containing two or more compounds or radicals supposed to act the part of a single one. [R.]
4. (Gram.) Agreeing in derivation and radical signification; -- said of words.
5. (Math.) Presenting themselves simultaneously and having reciprocal properties; -- frequently used in pure and applied mathematics with reference to two quantities, points, lines, axes, curves, etc.
{Conjugate axis of a hyperbola} (Math.), the line through the center of the curve, perpendicular to the line through the two foci.
{Conjugate diameters} (Conic Sections), two diameters of an ellipse or hyperbola such that each bisects all chords drawn parallel to the other.
{Conjugate focus} (Opt.) See under {Focus}.
{Conjugate mirrors} (Optics), two mirrors so placed that rays from the focus of one are received at the focus of the other, especially two concave mirrors so placed that rays proceeding from the principal focus of one and reflected in a parallel beam are received upon the other and brought to the principal focus.
{Conjugate point} (Geom.), an acnode. See {Acnode}, and {Double point}.
{Self-conjugate triangle} (Conic Sections), a triangle each of whose vertices is the pole of the opposite side with reference to a conic.