Given four parallel lines \( L_{1}, L_{2}, L_{3} \) and \( L_{4} \) as shown in figure. Let \( d_{i j} \) denote the perpendicular distance between lines \( L_{i} \) and \( L_{j} i, j \in\{1,2,3,4\} \). Let \( P \) be a point, sum of whose perpendicular
\( \mathrm{P} \) distances from four lines is \( K \), also \( d_{12}d_{23}d_{34} \) Then the complete locus of point \( P \).
W
\[
\begin{array}{l}
L_{1} \\
L_{2} \\
{ }^{L} \\
{ }_{3} \\
{ }^{L}
\end{array}
\]
\begin{tabular}{|l|l|l|l|}
\hline & \multicolumn{1}{|c|}{ Column-I } & \multicolumn{1}{|c|}{ Column-II } \\
\hline (a) & If \( K=d_{12}+2 d_{23}+d_{34} \) & (p) & Not possible \\
(b) & If \( \quad K=d_{12}+2 d_{23}+d_{34}+2 \alpha \) & (q) & Entire region between the lines \( L_{2} \) and \( L_{3} \) \\
where \( 0\alphad_{12} \) \\
(c) & \( \begin{array}{l}\text { If } \quad K=d_{12}+2 d_{23}+d_{34}+2 \alpha \\
\text { where } 0\alphad_{34}\end{array} \) & (r) & Entire region between the lines \( L_{1} \) and \( L_{2} \) \\
(d) & If \( Kd_{12}+2 d_{23}+d_{34} \) & (s) & \( \begin{array}{l}\text { Entire region between the lines } L_{1} \text { and } L_{2} \text { and } \\
\text { between } L_{3} \text { and } L_{4}\end{array} \) \\
\hline
\end{tabular}
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