The eccentricity of the hyperbola whose lengt | vedclass

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Question

We have $\frac{2 b^{2}}{a}=8$

and $2 b=\frac{1}{2}(2 a e)$

$	herefore \frac{2}{a}\left(\frac{a e}{2}ight)^{2}=8$

$a e^{2}=16--(1)$

Now

Vedclass · Accepted Answer

$\frac{2}{{\sqrt 3 }}\;$

Vedclass · Answer

We have $\frac{2 b^{2}}{a}=8$

and $2 b=\frac{1}{2}(2 a e)$

$	herefore \frac{2}{a}\left(\frac{a e}{2}ight)^{2}=8$

$a e^{2}=16--(1)$

Now $\frac{2 b^{2}}{a}=8$

$b^{2}=4 a$

$a^{2}\left(e^{2}-1ight)=4 a$

$a e^{2}-a=4$

Substitute the value of $a e^{2}=16$ in eq $(1)$

$16-a=4$

$-a=4-16$

$-a=-12$

$a=12$

$a e^{2}=16$

$e^{2}=\frac{16}{12}$

$e^{2}=\frac{4}{3}$

$e=\frac{2}{\sqrt{3}}$

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 :

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