The eccentricity of the hyperbola `x^2-4y^2=1` is a.`(sqrt(3))/2` b. `(sqrt(5))/2` c. `2/(sqrt(3))` d. `2/(sqrt(5))`

Explanation

For hyperbola `frac{x^{2}}{a^{2}}-frac{y^{2}}{b^{2}}=1`

As we know

`e=frac{c}{a}`, where `c=sqrt{a^{2}+b^{2}}`

Here, `a=1` and `b=frac{1}{2}`

`c=sqrt{1^{2}+(frac{1}{2})^{2}}`

`Rightarrow c=sqrt{1+frac{1}{4}}`

`Rightarrow c=sqrt{frac{5}{4}}`

`Rightarrow c=frac{sqrt{5}}{2}`

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