If the hyperhola x^2/a^2 - y^2/b^2 = 1 p...

If the hyperhola `x^2/a^2 - y^2/b^2 = 1` passes through the intersection of `7x+13y-87=0 and 5x-8y+7=0` and its latus rectum is `32sqrt(2)/(5)`, then value of `a` and `b` are respectively. (A) `5/sqrt(3), 2` (B) `5/sqrt(2), 4` (C) `3/sqrt(2), 4` (D) `2, sqrt(3)/5`

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The correct Answer is:

`a = 5/sqrt2, b = 4 `

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