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Let the latus rectum of the hyperbola x29- y2b2=1 subtend an angle of 3 at the centre of the hyperbola. If b2 is equal to lm(1+ n), where l and m are co-prime numbers, then l2+m2+n2 is equal to .
182
a=3; ends of latus rectum L (ae, b2a ), L' (ae, - b2a )
[figure]
'= 3 = 6
6= b2/aae b29e= 1 3 e= 3 b29
e2=1+ b29 3b481=1+ b29 b4-3b2-27=0
b2>0 b2= 3+ 9+1082= 32 (1+ 13 )
l=3, m=2, n=13 l2+m2+n2=9+4+169=182
Answer: 182
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