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A circle passes through the end of a diameter of ellipse (x2/a2 + y2/b2)=1 and also touches the curve. Prove that the locus of its centre is the ellipse 4(a2x2+b2y2)=(a2-b2).

A circle passes through the end of a diameter of ellipse (x2/a2 + y2/b2)=1 and also touches the curve. Prove that the locus of its centre is the ellipse 4(a2x2+b2y2)=(a2-b2).

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Grade:12th pass

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