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We know the slope of the normal which is (-1). This implies that the slope of the tangent is 1. Now,
y= mx+c is a tangent to y^2=4ax, iff. c=a/m.
Putting a=3, m=1, we get c=3.
Tangent is y=x+3.
Solving the equations of parabola and tangent, we get pts (3,6) and(3,-6)
This means that k=-3 or k=9
x + y = k
y = -x + k
slope of normal = -1
so slope of tangent = 1
parabola is y2 = 12x ..............1
2yy1 = 12
y1 = 1 so , y = 6
from eq 1 , if y = 6 then x = 3
x+y = k touches parabola at (3,6) so it will satisfy this eq
at (3,6) , k = 9
therefore value of k is 9
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