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Circle of constant radius r are draw to ...

Circle of constant radius r are draw to pass through the ends of a variable diameter of the ellipse `x^(2)/a^(2)+y^(2)/b^(2)=1`. Prove that locus of their centres is the curve
`(x^(2)+y^(2))(a^(2)x^(2)+b^(2)y^(2)+a^(2)b^(2))=r^(2)(a^(2)x^(2)+b^(2)y^(2))`

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The correct Answer is:
(h,k).
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