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 = +/-$\frac{b}{a}$x. The hyperbola lies between the asymptotes in two opposite sectors; the conjugate lies in the other two sectors.