The descending order of magnitude of the eccentricities of the following hyperbolas is A. A hyperbola whose distance between foci is three times the distance between its directrices. B. Hyperbola in which the transverse axis is twice the conjugate axis. C. Hyperbola with asymptotes x+y+1=0, x-y+3=0

Step-by-step solution

A: Distance between foci is three times the distance between its directrices. 2 a e=3 2 a e e^2=3 e= 3 =1.732 B : The transverse axis is twice the conjugate axis 2 a=2(2 b) a=2 b b= a 2 We know that a^2 e^2=a^2+b^2=a^2+ a^2 4 e^2= 5 4 e= 5 2 =1.11 C : Slope of asymptotes are m₁=-1 and m₂=1 aligned & m₁ m₂=-1, so it is rectangular hyperbola & e= 2 =1.414 aligned Hence order is A, C, B .