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Consider the family of circles x^2+y^2=...

Consider the family of circles `x^2+y^2=r^2, 2 < r < 5` . If in the first quadrant, the common tangnet to a circle of this family and the ellipse `4x^2 +25y^2=100` meets the co-ordinate axes at A and B, then find the equation of the locus of the mid-point of AB.

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