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Prove that the tangents to family of hyp...

Prove that the tangents to family of hyperbola`x^2/(b^2+lambda) - y^2/b^2 =1` (where `lambda` is a real parameter) at their point of intersection with `x^2-y^2= 2b^2 + lambda^2` are a pair of fixed lines. Find the equations of the lines.

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