Calculus In Parabola

Calculus Level 5

Let \(S\) be the Focus of \(y^2 = 4x\) and a point \(P\) is moving on this curve such that it's abscissa is increasing at the rate of \( 4 \) units per second, then the rate of increase of length of projection of \(SP\) on \( x + y =1\) when P is at \( (4,4) \) is \(\gamma\).

Find \(10^3\gamma \). Give your answer to 1 decimal place.

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