The eccentricity of the hyperbola whose latus rectum is half of its transverse axis is a.`1/(sqrt(2))` b. `sqrt(2/3)` c. `sqrt(3/2)` d. none of these

Explanation

Given

`frac{2 b^{2}}{a}=frac{1}{2} times 2 b`

`Rightarrow 2 b^{2}=a b`

`Rightarrow a=2 b`

Now, `e=sqrt{1-frac{b^{2}}{a^{2}}}`

`Rightarrow e=sqrt{1-frac{b^{2}}{4 b^{2}}}`

`Rightarrow e=sqrt{1-frac{1}{4}}`

`Rightarrow e=sqrt{frac{3}{4}}`

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