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If the latus rectum of a hyperbola forms...

If the latus rectum of a hyperbola forms an equilateral triangle with the vertex at the center of the hyperbola ,then find the eccentricity of the hyperbola.

Text Solution

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`(a^2e^2)/(a^2)-y^2/b^2=1`
`e^2-1=y^2/b^2`
`y^2=b^2(e^2-1)`
`y=pmbsqrt(e^2-1)`
`tan30^o=(AD)/(OD)`
`1/sqrt3=(bsqrt(e^2-1))/(ae)`
Squaring both sides
`1/3=(b^2(e^2-1))/(a^2e^2)`
...
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