Let \( S \) be the focus of \( y^{2}=4 x \) and a point \( P \) be moving on the curve such that...

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Let \( S \) be the focus of \( y^{2}=4 x \) and a point \( P \) be moving on the curve such that its abscissa is increasing at the
P rate of 4 units/s. Then the rate of increase of the projection of \( S P \) on \( x+y=1 \) when \( p \) is at \( (4,4) \) is
(a) \( -\sqrt{2} \)
(b) \( -\frac{3}{\sqrt{2}} \)
(c) \( -1 \)
(d) \( \sqrt{2} \)
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