A ray of light comes straight vertically down at \(x=a\) and reflects off the parabola \(y = cx^2\) according
to the usual principle of reflection (where \( c > 0\)). It bounces off the parabola and crosses the y-axis
at some point \(y = b\). Find \(b\) in terms of \(c\) and show that it is the same point regardless of where
the light is incident (that is, is independent of \(a\)). Do not look up any resources - solve from scratch.