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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

Verified by Experts

The correct Answer is:
`(1+sqrt(13))/(2sqrt3)`
`tan30^(@)=(b^(2)//a)/(ae)`
`"or "(e)/(sqrt3)=e^(2)-1`
`"or "sqrt3e^(2)-e-sqrt3=0`
`"or "e=(1pmsqrt(13))/(2sqrt3)`
`"or "e=(1+sqrt(13))/(2sqrt3)`
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