CONJUGATE (Lat. eonjugatus, p.p. of eon jugure, to join together, from coin-, together jugare. to yoke, from juguni, yoke; connected with Gk. rtry6v, , zgyo1., ()Church Slay. igo, Lith. jnngus, Guth. juk, Icel. ok, AS. geoc, Engl. yoke, OHG. job, Ger. Joeh, Skt, yuga, yoke). A term signifying united in pairs, and having various uses in mathematics. Conjuate MOM are num bers, real or imaginary, such as a + VT, and a--1/17. or a+ a—bi, satisfying a giNen equa tion. ( See COMPLEX Nur BER. ) angles are any two angles whose sum is 360°, as 10° and 350°, 400° and —40°, 180° and 180''. Con jugate points with respect to a conic are points each of which lies on the polar of the other. (Sec CIRCLE.) A conjugate hyperbola is one which has for its transverse and conjugate diameters the conjugate and transverse diameters of a given hyperbola. The equations of an hyperbola and its conjugate hyperbola are related thus: 11 1 be the equation of the given hyper bola, then 67 = — 1 is the equation of its conjugate. Conjugate /incs, with respect to a
are lines each of which passes through the pole of the other. axes or diameters of a conic are diameters which are conjugate with respect to the conic. Conjugate triangles with respect to a conic are triangles such that the sides of each are the polars of the vertices of the other and the vertices of each are the poles of the sides of the other. Conjugate points in a harmonic range are a pair of pomtsharmonically separating two others. Thus, if A, P, B, Q, are four collinear points such thatAP:PB=.AQ:BQ, P and Q are called harmonic conjugates. Simi larly in a harmonic pencil of four rays 0 (APBQ), OP and OQ are conjugate rays. (See ANIIARMONIC RATIO.) Conjugate elements of a determinant (q.v.) are those elements which are symmetrically situated with respect to the prin cipal diagonal. Certain forms of qualities are also called conjugate.