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 \( \lambda\left(\lambda \in \mathrm{R}^{+}\right) \), then the locus of point \( P \) is:
(a) \( x^{2}=\lambda c^{2} \)
(b) \( y^{2}=\lambda c^{2} \)
(c) \( x y=\lambda c^{2} \)
(d) \( y^{2}=\lambda c^{3} \)
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