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The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half of the distance between the foci is
A. 4/3

B. $\frac{4}{\sqrt{3}}$
C. $\frac{2}{\sqrt{3}}$
D. none of these

Answers (1)

Let the equation of the hyperbola be x²/a²-y²/b²=1

length of latus rectum=8

2b²/a=8

b²=4a

Conjugate axis=half of the distance between the foci

2b=ae

b²=a²(e²-1)

$\frac{a^{2}e^{2}}{4}$ =a²(e²-1)

e²=4/3

e= $\frac{2}{\sqrt{3}}$

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infoexpert22

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