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Chords of the circle x^(2)+y^(2)=4, touc...

Chords of the circle `x^(2)+y^(2)=4`, touch the hyperbola `(x^(2))/(4)-(y^(2))/(16)=1`.The locus of their middle-points is the curve `(x^(2)+y^(2))^(2)=lambdax^(2)-16y^(2)`, then the value of `lambda` is

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