Passage-I A point moves such that the sum of the slopes of the normal drawn from it to the hyper....

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Passage-I
A point \( \mathrm{P} \) moves such that the sum of the slopes of the normal drawn from it to the hyperbola \( x y=16 \) is equal to
\( \mathrm{P} \)
the sum of ordinates of feet of normal. The locus of \( \mathrm{P} \) is a curve \( \mathrm{C} \).

If the tangent to the curve \( \mathrm{C} \) cuts the coordinate axis at \( \mathrm{A} \) and \( \mathrm{B} \), then the locus of the middle point of \( \mathrm{AB} \) is
(1) \( x^{2}=4 y \)
(2) \( x^{2}=2 y \)
(3) \( x^{2}+2 y=0 \)
(4) \( x^{2}+4 y=0 \)


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