Circular conundrum

Geometry Level 4

\[ \begin{cases} {x^2+y^2+3x+7y+2p-5=0} \\ {x^2+y^2 + 2x+2y-p^2 = 0 } \end{cases} \]

If \(P\) and \(Q\) are the points of intersection of the circles given above for constant \(p\), then there is a circle passing through \(P,Q\) and \((1,1)\) for:

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