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Prove that the locus of the middle poin...

Prove that the locus of the middle points of normal chords of the ellipse `x^(2)/a^(2)+y^(2)/b^(2)=1` is the curve `(x^(2)/a^(2)+y^(2)/b^(2))(a^(6)/x^(2)+b^(6)/y^(2))=(A^(2)-B^(2))^(2)`

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