The conjugate of x^2/a^2 - y^2/b^2 = 1 is -x^2/a^2 + y^2/b^2 = 1, or equivalently y^2/b^2 - x^2/a^2 = 1. It has transverse axis along y, semi-transverse axis b, semi-conjugate axis a. Its eccentricity e2 satisfies 1/e1^2 + 1/e2^2 = 1. Both the hyperbola and its conjugate share the same asymptotes y = +/-(b/a)x. The hyperbola lies between the asymptotes in two opposite sectors; the conjugate lies in the other two sectors.