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The hyperbola x^2 a^2 - y^2 b^2 =1 passes through the point of intersection of the lines x-3 5 y=0 and 5 x-2 y=13 and the length of its latus rectum is 4 / 3 units. Then the value of 9 e ^2-1 where e is the eccentricity of the hyperbola is

Correct answer

9

Step-by-step solution

The line x-3 5 y=0 and 5 x-2 y=13 intersect at the point. Since the given hyperbola passes through this point, (3 5 )^2 a^2 1 b^2 =1 or 45 a^2 - 1 b^2 =1 ....(1) Also length of the latus rectum = 2 b^2 a = 4 3 (given) .....(2) From (1) and (2) we get 45 a^2 - 3 2 a =1 a =6 or - 15 2 a 0 therefore we have a=6 b^2=4

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