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  • 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  <div cla

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
 

Option: 1

\frac{4}{3}


Option: 2

\frac{4}{\sqrt{3}}


Option: 3

\frac{2}{\sqrt{3}}


Option: 4

\sqrt{3}


Answers (1)

best_answer

We have  \mathrm {2 b=a e\: \: and \: \: \frac{2 b^2}{a}=8}  


Also, we have  \mathrm {b^2=a^2\left(e^2-1\right)} 

Now eliminating  \mathrm {a} and  \mathrm {b} from these equations
\mathrm { \frac{e^2}{4}=e^2-1 \Rightarrow 4=3 e^2 \quad \therefore \quad e=\frac{2}{\sqrt{3}} \text { as } e>0 }

Posted by

Rishabh

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