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Question

The eccentricity of the hyperbola whose latus-return is 8 and length of the conjugate axis is equal to half the distance between the foci, is

A
43
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B
43
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C
23
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D
None of these
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Solution

The correct option is C 23
Given that the length of the latus rectum is 8 and length of the conjugate axis is equal to half the distance between the foci.

2b2a=8 and 2b=12(2ae)

2a(ae2)2=8

ae2=16 ...(1)

We have 2b2a=8

b2=4a

a2(e21)=4a

ae2a=4

16a=4 (by (1))

a=12

Substitute a=12 in (1)

12e2=16

e2=43

e=23

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