If a circle passes through the point \( (r', \theta') \) and touches the initial line a distance \(c\) from the pole, and its polar equation is

\[ r^2 - 2cr + c^2 = \lambda (r'^2 - 2cr' + c^2) \; , \]

then find the value of \( \lambda\) in terms of \( r,r', \theta, \theta' \).

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