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) =`

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

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 .

If e_(1) and e_(2) are the eccentricities of two conics with e_(1)^(2) + e_(2)^(2) = 3 , then the conics are

If e_(1) is the eccentricity of the conic 9x^(2)+4y^(2)=36 and e_(2) is the eccentricity of the conic 9x^(2)-4y^(2)=36 then e12-e22=2 b.e22-e12=2c.2 3

If e_(1) is the eccentricity of the hyperbola (x^(2))/(36)-(y^2)/(49) =1 and e_(2) is the eccentricity of the hyperbola (x^(2))/(36)-(y^2)/(49) =-1 then

An ellipse and a hyperbola are confocal (have the same focus) and the conjugate axis of the hyperbola is equal to the minor axis of the ellipse.If e_(1) and e_(2) are the eccentricities of the ellipse and the hyperbola,respectively, then prove that (1)/(e_(1)^(2))+(1)/(e_(2)^(2))=2

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