Hi, can anyone please help me with this question? I have no idea how to start.

(a) Consider the map . Prove that under , lines parallel to the real axis are mapped to parabolas.

(b) Consider the map , for some branch of the square root. Prove that under lines parallel to the real axis are mapped to hyperbolas.

I did try to do the questions, so I substitute , then get , but I really don't know how to show this mapping thing. Please help me. Thanks a lot.