I'm working on a project regarding plane curves and I need to reparameterizate these two curves using

**arc lenght**

Ellipse: c(t)=(2sint, cost)

Parabola: y=x^2/2

I solved the ellipse, but I don't know if it's the right answer, my solution is c1(s)=(2sin*s/2, cos*s/2)

Also the professor said there is a problem in one of these 2, but I don't know which one, one is maybe unsolvable?

English is not my native language, so sorry if I missed out on some math terminology

Thank you