If latus rectum of the hyperbola is half of its transverse axis, then its eccentricity is

  • Option 1)

    3/2

  • Option 2)

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

  • Option 3)

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

  • Option 4)

    none of these

 

Answers (1)

\frac{2b^{2}}{a}=\frac{2b}{2}

\Rightarrow 2b=a

Also, b^{2}-a^{2} (e^{2}-1)

\Rightarrow \frac{1}{4} = e^{2}-1

\Rightarrow e^{2}=\frac{5}{4}\Rightarrow e\frac{\sqrt{5}}{2}


Option 1)

3/2

This solution is incorrect

Option 2)

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

This solution is incorrect

Option 3)

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

This solution is incorrect

Option 4)

none of these

This solution is correct

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