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  • A hyperbola has its axes along the coordinate axes. The distance between the focii is 9 and its eccentricity is <img alt="\mathrm{\sqrt{3}}" src="https://entrancecorner.oncodecogs.co

A hyperbola has its axes along the coordinate axes. The distance

between the focii is 9 and its eccentricity is \mathrm{\sqrt{3}} . The length of its

latus rectum is \mathrm{\lambda \sqrt{3}}. Then the value of \mathrm{\lambda } is

Option: 1

6


Option: 2

3


Option: 3

4


Option: 4

8


Answers (1)

best_answer

Given,   \mathrm{2 a e=9, e=\sqrt{3} \therefore a=\frac{3 \sqrt{3}}{2}}

Latus rectum = \mathrm{\frac{2 b^2}{a}=2 a\left(e^2-1\right)=3 \sqrt{3}(3-1)=6 \sqrt{3} .}

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