If `e` and `e'` are the eccentricities of the hyperbola `x^(2)/a^(2)-y^(2)/b^(2)=1` and its conjugate hyperbola,the value of `1/e^(2)+1/e^prime2` is

If e and e\' are the eccentricities of the hyperbola x^2/a^2 - y^2/b^2 = 1 and its conjugate hyperbola, prove that 1/e^2 + 1+e\'^2 = 1

If e_(1) and e_(2) are the eccentricities of a hyperbola 3x^(2)-2y^(2)=25 and its conjugate, then

If e_(1)ande_(2) be the eccentricities of the hyperbola xy=c^(2)andx^(2)-y^(2)=c^(2) respectively then :

If e and e_(1) , are the eccentricities of the hyperbolas xy=c^(2) and x^(2)-y^(2)=c^(2) , then e^(2)+e_(1)^(2) is equal to

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

If e and e' are the eccentricities of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and (y^(2))/(b^(2))-(x^(2))/(a^(2))=1, then the point ((1)/(e),(1)/(e')) lies on the circle (A) x^(2)+y^(2)=1(B)x^(2)+y^(2)=2(C)x^(2)+y^(2)=3(D)x^(2)+y^(2)=4

If e and e_(1) are the eccentricities of xy=c^(2),x^(2)-y^(2)=a^(2) then e^(4)+e_(1)^(4)=