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Question

The eccentricity of the hyperbola with length of the latus rectum as 8 and the length of its conjugate axis is equal to half of the distance between its foci , is

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Solution

solution:-
In hyperbola length of latus rectum=2b2a

2b2a=8 ……….(1)

Length of conjugate axis=12 (distance between the foci)

2b=12(2ae)

b=ae2

Now substituting in (1) we get

2a×a2e24=8

ae2=16 ……….(3)

But 2b2a=8

b2=4a

a(e21)=4 ……..(4)

Now 16a=4

a=12 from 3,

12e2=16

e=23.


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