A point \( P \) moves such that sum of the slopes of the normals drawn from it to the hyperbola ...

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A point \( P \) moves such that sum of the slopes of the normals drawn from it to the hyperbola \( x y=16 \) is equal to the sum of the ordinates of the feet of the normals. Let \( P \) lies on the curve
\( \mathrm{P} \) \( C \), then:

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The equation of \( C \) is :
(a) \( x^{2}=4 y \)
(b) \( x^{2}=16 y \)
(c) \( x^{2}=12 y \)
(d) \( y^{2}=8 x \)
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