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Circle S(1) is centered at (0,3) with ra...

Circle `S_(1)` is centered at (0,3) with radius 1. Circle `S_(2)` is externally tangent to circle `S_(1)` and also tangent to x-axis.If the locus of the centre of the variable circle `S_(2)` can be expressed as `y =1+ ( x^(2))/( lambda)` . Find `lambda`

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