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Show that the locus of the midpoints of ...

Show that the locus of the midpoints of the chords of the circle `x^(2)+y^(2)=a^(2)` which are tangent to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` is `(x^(2)+y^(2))^(2)=a^(2)x^(2)-b^(2)y^(2)`.

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