A line L:y=mx+3 meets the y-axis at E(0,3) and the are of the parabola `y^(2)=16x,0leyle9`, at the point `F(x_(0),y_(0))`. The tangent to the parabola at `F(x_(0),y_(0))` intersects the y-axis at `G(0,y_(1))`. The slope m of the line L is chosen such that area of triangle EFG has a local maximum.