I would not normally stop to answer this question, mainly because there is no question asked. It's just three statements.
I do have to stop here and leave a remark, however.
Math and Physics are closely enough related that I would not have expected to see what I see here. Although the math in this question is reasonable, the Physics is inexcusable.
A rainbow is always a part of a circle. Rainbows are never parabolas.
You could never cut a parabola out of paper, and then hold it up in front of you after a rainstorm, and match it to the rainbow.