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A line \( \mathrm{L}: \mathrm{y}=\mathrm{mx}+3 \) meets \( y \) - axis at \( \mathrm{E}(0,3) \) and the arc of the parabola \( y^{2}-16 x, 0 \leq y \leq 6 \) at the point \( F\left(x_{0}, y_{0}\right) \).
\( P \) The tangent to the parabola at \( F\left(x_{0}, y_{0}\right) \) intersects the \( y \) -

W axis at \( G\left(0, y_{1}\right) \). The slope \( m \) of the line \( L \) is chosen such that the area of the triangle EFG has a local maximum Match L.ist I with List II and select the correct answer using the code given below the lists :
[JEE Advanced-2013]
List - I List - II
P. \( m= \)
1. \( \frac{1}{2} \)
Q. Maximum area of
2. 4
\( \triangle \mathrm{EFG} \) is
R. \( \mathrm{y}_{0}=3.2 \)
S. \( y_{1}= \)
4. 1
Codes: \( P \quad Q \quad \) R \( \quad \) S
(A) \( 4 \quad 1 \quad 2 \quad 3 \)
(B) \( 3 \quad 4 \quad 1 \quad 2 \)
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