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Question

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

A
43
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B
43
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C
23
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D
3
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Solution

The correct option is B 23
length of latus rectum=8 ....Given

So, 2b2a=8

Length of conjugate axis = Half of distance between focii

So, 2b=ae

e=2ba

2ba×b=8

e×b=8 ; b=8e

a=2be=16e2

e=1+b2a2=    1+64e216×16e4

e=1+e24

e2=1+e24

4e2=4+e2

e2=43

e=23

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