Change from cartesian coordinates to cylindrical and spheric

[akkex]

Hello, I have 6 equations in Cartesian coordinates a) change to cylindrical coordinates b) change to spherical coordinate
This book show me the answers but i don't find it
If anyone can help me i will appreciate so much!
Thanks for your time


1) z = 2 a) z = 2 b)ρcos(Φ) = 2

2) z = 5x² + 5y² a) z = 5r² b)5ρ = cos(Φ)cosec²(Φ)

3) x² + y² + z² = 9 a) r² + z² = 9 b)ρ = 3

4) x² + y² + 2z² = 4 a) r² +2z² = 4 b)ρ² (1 + cos²(Φ) = 4

5) x² - y² -2z² = 1 a) 2z² = r²cos(2θ) b)ρ² (sin²(Φ)cos(2θ) -2cos²(Φ) = 1

6) x² + y² = 2x a) r = 2cos(θ) b)ρsin(Φ) = 2cos(θ)

[akkex]

I can do the first because from Cartesian coordinates to a) z = z in cylindrical coordinates and b) z = ρcos(Φ) in spherical coordinates. But in the other exercises i can't find a way to solve it