If the sum of the slopes of the normal from a point \( P \) to the hyperbola \( x y=c^{2} \) is ...

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If the sum of the slopes of the normal from a point \( P \) to the hyperbola \( x y=c^{2} \) is equal to \( \lambda\left(\lambda \in R^{+}\right) \), then locus of point \( P \) is
(a) \( x^{2}=\lambda c^{2} \)
(b) \( y^{2}=\lambda c^{2} \)
(c) \( x y=\lambda c^{2} \)
(d) None of these
\( P \)
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