Comparison of Hyperbola and its conjugate hyperbola

If a,b are eccentricities of a hyperbola and its conjugate hyperbola then a^(-2)+b^(-2)=

If a,b are eccentricities of a hyperbola and its conjugate hyperbola then a^(-2)+b^(-2)=

If e and e' are the eccentricities of a hyperbola and its conjugate hyperbola respectively then prove that 1/e^2+1/(e')^2=1

A hyperbola and its conjugate have the same assymptote and The equation of the pair of assymptotes differ from the equation of hyperbola and the conjugate hyperbola by some constant only.

If e_(1) and e_(2) are the eccentricities of the hyperbola and its conjugate hyperbola respectively then (1)/(e_(1)^(2))+(1)/(e_(2)^(2)) is equal to

Prove that any hyperbola and its conjugate hyperbola cannot have common normal.

Prove that any hyperbola and its conjugate hyperbola cannot have common normal.

Prove that any hyperbola and its conjugate hyperbola cannot have common normal.

Prove that any hyperbola and its conjugate hyperbola cannot have common normal.

Statement-I A hyperbola and its conjugate hyperbola have the same asymptotes. Statement-II The difference between the second degree curve and pair of asymptotes is constant.