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From a point on the circle x^2+y^2=a^2 ,...

From a point on the circle `x^2+y^2=a^2` , two tangents are drawn to the circle `x^2+y^2=b^2(a > b)` . If the chord of contact touches a variable circle passing through origin, show that the locus of the center of the variable circle is always a parabola.

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