Consider the system of hyperbola `xy = k, k in R`. Let `e_1` be the eccentricity when k = 4 and `e_2` be the eccentricity when k = 9, then `e_1-e_2`

Consider the set the of hyperbola xy = k, k in R . Let e_(1) be the eccentricity when k = 4 and e_(2) be the eccentricity when k = 9 then e_(1) - e_(2) =

Consider an ellipse x^2/a^2+y^2/b^2=1 Let a hyperbola is having its vertices at the extremities of minor axis of an ellipse and length of major axis of an ellipse is equal to the distance between the foci of hyperbola. Let e_1 and e_2 be the eccentricities of an ellipse and hyperbola respectively. Again let A be the area of the quadrilateral formed by joining all the foci and A, be the area of the quadrilateral formed by all the directrices. The relation between e_1 and e_2 is given by

If e be the eccentricity of ellipse 3x2+2xy+3y^(2)=1 then 8e^(2) 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 .

Statement-I (5)/(3) and (5)/(4) are the eccentricities of two conjugate hyperbolas. Statement-II If e_1 and e_2 are the eccentricities of two conjugate hyperbolas, then e_1e_2gt1 .

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 .