Let e be the eccentricity of a hyperbola and f(e ) be the eccentricity of its conjugate hyperbola then `int_(1)^(3)ubrace(fff...f(e))_("n times")` de is equal to

Let e be the eccentricity of a hyperbola and f(e) be the eccentricity of its conjugate hyperbola then int_0^2 fff....f(e) n times de is equal to A) 2sqrt(2) if n is odd B) 4 if n is odd C) 2sqrt2 if n is even D)3 if n is even

If the eccentricity of a hyperbola is sqrt(3) , the eccentricity of its conjugate hyperbola, is

If the eccentricity of a hyperbola is (5)/(3) .Then the eccentricity of its conjugate Hyperbola is

If the eccentricity of a hyperbola is 2, then find the eccentricity of its conjugate hyperbola.

If e_(1) be the eccentricity of a hyperbola and e_(2) be the eccentricity of its conjugate, then show that the point (1/e_(1) , 1/e_(2)) lies on the circle x^(2) + y^(2) = 1 .

Statement-I If eccentricity of a hyperbola is 2, then eccentricity of its conjugate hyperbola is (2)/(sqrt(3)) . Statement-II if e and e_1 are the eccentricities of two conjugate hyperbolas, then ee_1gt1 .

Consider the hyperbola y = x-1/x. Its eccentricity is

Statement- 1 : If 5//3 is the eccentricity of a hyperbola, then the eccentricity of its conjugate hyperbola is 5//4 . Statement- 2 : If e and e' are the eccentricities of hyperbolas (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and (x^(2))/(a^(2))-(y^(2))/(b^(2))=-1 respectively, then (1)/(e^(2))+(1)/(e'^(2))=1 .