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Prove that the locus of the pole with re...

Prove that the locus of the pole with respect to the hyperbola `(x^(2))/(a^(2)) - (y^(2))/(b^(2)) = 1` of any tangent to the circle, whose diameter is the line joining the foci, is the ellipse `(x^(2))/(a^(4)) + (y^(2))/(b^(4)) = (1)/(a^(2) + b^(2))`.

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