Since you have managed to work out all other parts, I believe you have had a quite good understanding of the question. So I only give you a few hints and don't need to waste time posting the full solution.
1. Find the equation of the locus as required by the question ( I think you have obtained it? good )
2. If indeed this line ( the locus) is a normal, at which point must this normal be? i.e., find x0, so that at x=x0, the gradient of normal equals to the gradient of this line ( the locus)
3. Then find y0=x0^2/4a, and use point-gradient formula to write the normal at the point (x0,y0)
4. Does the normal coincide with the equation of the locus? Yes? good, u got it.
