Discussion Forum

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 

Answer:

Explanation:

We have ,  $\frac{2b^{2}}{a}=8$ and 2b=ae

$\Rightarrow b^{2}=4a$ and 2b=ae

consider 2b=ae

$\Rightarrow 4b^{2}=a^{2}e^{2}$

$\Rightarrow 4a^{2}(e^{2}-1)=a^{2}e^{2}$

$\Rightarrow 4e^{2}-4=e^{2} [\therefore a\neq 0]$

$\Rightarrow 3e^{2}=4$

$\Rightarrow e=\frac{2}{\sqrt{3}}   [\because e>0]$