Let each of the circles, \[ \begin{array}{l} S_{1} \equiv x^{2}+y^{2}+4 y-1=0, \\ S_{2} \equiv x....

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Let each of the circles,
\[
\begin{array}{l}
S_{1} \equiv x^{2}+y^{2}+4 y-1=0, \\
S_{2} \equiv x^{2}+y^{2}+6 x+y+8=0, \\
S_{3} \equiv x^{2}+y^{2}-4 x-4 y-37=0
\end{array}
\]
\( \mathrm{P} \)
Touches the other two. Let \( \mathrm{P}_{1}, \mathrm{P}_{2}, \mathrm{P}_{3} \) be the points of contact of \( S_{1} \) and \( S_{2}, S_{2} \) and \( S_{3}, S_{3} \) and \( S_{1} \) respectively and \( C_{1}, C_{2}, C_{3} \) be the centres of \( S_{1}, S_{2}, S_{3} \) respectively.
\( P_{2} \) and \( P_{3} \) are image of each other with respect to line:
(1) \( y=x+1 \)
(2) \( y=-x \)
(3) \( y=x \)
(4) \( y=-x+2 \)
.


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