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Question

If the latus rectum of a hyperbola through one focus subtends 60 angle at the other focus, then its eccentricity e is
 


Solution

The correct option is B
Let LSL be a latus rectum through the focus S (ae, 0)of the hyperbola x2a2y2b2=1. It subtends angle 60 at
   the other focus S(ae,θ)

We have,  LSL=60
   LSS=30    
In ΔLSS we have
    tan 30=LSSS13=b2/a2ae
     13=b22a2e
     13=e212e
     3e22e3=0
    (e3)(2e+1)=0
     3 

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