Find the eccentricity of the hyperbola whose latusrectum is half of its transverse axis.

Explanation

We have given latus rectum is half of its transverse axis of a hyperbola.


Now take the equation of hyperbola`x^2/a^2− y^2/b^2=1`

Then transverse axis =`2a` and latus rectum =`(2b^2)/a`

Now here,` (2b^2)/a=(1/2)*2a`

`implies 2b^2=a^2`

Therefore, `e^2=1+(b^2/a^2)`

`e^2=1+(b^2/(2b^2))`

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