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 for Conjugate axis of a hyperbola
From The Collaborative International Dictionary of English v.0.48 :

  Conjugate \Con"ju*gate\, a. [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.
        [1913 Webster]
     2. (Bot.) In single pairs; coupled.
        [1913 Webster]
     3. (Chem.) Containing two or more compounds or radicals
        supposed to act the part of a single one. [R.]
        [1913 Webster]
     4. (Gram.) Agreeing in derivation and radical signification;
        -- said of words.
        [1913 Webster]
     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.
        [1913 Webster]
     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.
        [1913 Webster]

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