Find the locus of the mid-point of chords of the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{...

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Find the locus of the mid-point of chords of the ellipse \( \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(ab) \) passing through the point \( (2 a, 0) \).
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