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Prove that the locus of the middle-point...

Prove that the locus of the middle-points of the chords of the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` which pass through a fixed point `(alpha, beta)` is a hyperbola whose centre is `((alpha)/(2), (beta)/(2))`.

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