If e₁, e₂ are respectively the eccentricities of the curves 9 x^2-16 y^2-144=0 and 9 x^2-16 y^2+144=0 , then e₁^2 e₂^2 e₁^2+e₂^2 =

Step-by-step solution

(i) is a hyperbola and (ii) is a conjugate hyperbola, We have, array ll & 1 e₁^2 + 1 e₂^2 =1 & e₁^2+e₂^2 e₁^2 e₂^2 =1 e₁^2 e₂^2 e₁^2+e₂^2 =1 array Hence, option (b) is correct.