Step-by-Step Solution
Key Concept: The normal to a parabola at parameter $t$ has equation $x + ty = 2at + at^3$, and solving for concurrent normals uses parameter relations.
Let $A = (at_1^2, 2at_1)$ and $B = (at_2^2, 2at_2)$ with the foot of the normal at $(at_3^2, 2at_3)$. The normal at a point has the property that $2at_3 = -fa$ and $t_3 = -t_1$ and $t_2 = -3$ and $-2 - 3 - t_3 = 0$, giving $t_1 = 5$. The equation of the normal becomes $5x + y - 135a = 0$.
Correct Answer: 1