If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is

Answer

2

Explanation

Let hyperbola `(x ^(2))/(a ^(2)) - (y^(2))/(b ^(2)) =1`
Given `2b =5, 2 ae, =13`
`because b ^(2) =a^(2) (e ^(2) -1)`
`4b ^(2) = 4 a ^(2) e ^(2) -4a ^(2)`
`25-169 -4a ^(2)`
`a=6`
Put `a =6and b = 5/2 in b ^(2) =a ^(2) (e ^(2) -1) implies e = (13)/(12).`