Why does the rainbow appears as a parabola?

The Rainbow is not a parabola. It is part of a circle. The Rainbow is seen at all points where the angle between the sunlight ( light directly from the sun) and the refractured light to your eyes have a fixed angle. 40° an 42°. read more

A rainbow will always appear at a specified angle from you and a lightsource which is dictated by the angle of total internal reflection of the waterdroplets in the atmosphere. Thus, the only satisfactory answer that allows the production of this total internal reflection is a circle. Side note: Every rainbow is a double rainbow. read more