Statement 1: If $\sec \theta ,\theta \in \left(\frac{-\pi }{2},\frac{\pi }{2}\right)$ represent eccentricity of a hyperbola then eccentricity of its conjugate hyperbola is given by $\mathrm{cosec}\theta .$

Statement 2: If $e_1,e_2$ are eccentricities of two hyperbolas which are conjugate to each other then $e_1^{-2}+e_2^{-2}=1$.