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

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