I know this won't be much help but this is one of those conceptual problems that it will really benefit you to puzzle through on your own.

Start by sketching some bits of curve and seeing where their normal lines go. Then try to arrange those bits of curve so that the normal lines all intersect at the same point.

Eventually the shape those bits of curve need to make when joined will be obvious.

Remember a curve can go any which way in the plane. It doesn't have to look like a function.