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

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If the sum of the slopes of the normals from a point \( P \) to the hyperbola \( x y=c^{2} \) is equal to \( \lambda\left(\lambda \in R^{+}\right) \), then
\( \mathrm{P} \) locus of point \( P \) is

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(a) \( x^{2}-y^{2}=\lambda c^{2} \)
(b) \( y^{2}=\lambda c^{2} \)
(c) \( x y=\lambda c^{2} \)
(d) \( x^{2}=\lambda c^{2} \)
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