Circles in Polar Coordinates too

Geometry Level pending

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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