Question

Find a parametrization of cylinder. x^2+〖(y-4)〗^2=16, 0≤z≤5

Answer 1

$$x=4\cos \theta, y-4=4\sin \theta$$

The cylinder $x^2+(y-4)^2=16, 0\leq z\leq5$ is parametrized as

$$\bold{r}(\theta, z)=\langle4\cos\theta, 4+4\sin\theta,z\rangle,$$

$$\theta\in(0, 2\pi], z\in[0,5]$$