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

The hyperbola `x^2/a^2 - y^2/a^2 - y^2/b^2 = 1` passes through the point of intersection of the lines `7x+ 13y-87=0 and 5x-8y+7=0` and its latus rectum is `32sqrt(2)/5`. Find `a and b`.

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The correct Answer is:
`a = 5/sqrt2, b = 4 `
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