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The hyperbola (x^(2))/(a^(2))-(y^(2))/(b...

The hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2)) = 1` passes through the point of intersection of the lines x + y = 3, 2x - 3y = 1. and its eccentricity is `sqrt(3)`, show that its length of latus rectum is `2sqrt(14)`.

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