\[ \begin{array}{l} P: x^{2}-y^{2}+2 y-1=0 \\ L: x+y=3 \end{array} ...

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\[
\begin{array}{l}
P: x^{2}-y^{2}+2 y-1=0 \\
L: x+y=3
\end{array}
\]
If \( L^{\prime} \) represents the line perpendicular to \( L \) passing through the point of intersection of the pair of lines \( P \), then equation of the pair of lines representing \( L \) and \( L^{\prime} \) is
(a) \( x^{2}-y^{2}-4 x+2 y+3=0 \)
(b) \( x^{2}-y^{2}-2 x+4 y-3=0 \)
(c) \( x^{2}-y^{2}+2 x-4 y-3=0 \)
(d) \( x^{2}-y^{2}+4 x-2 y+3=0 \)
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