Find a parametric representation for the lower half of the ellipsoid $4x^2 +4y^2 +z^2 = 4$. Then find the area of this surface. [closed]

Find a parametric representation for the lower half of the ellipsoid $$4x^2 +4y^2 +z^2 = 4$$. Then find the area of this surface.

(I couldn't do my school homework, can you help me in detail, thank you in advance.)

• So far all 6 posts of you have been no-clue-do-my-homework questions. See How to ask a good question.
– Saad
Jun 17 '20 at 2:56

1 Answer

$$x^2+y^2 + z^2/4 = 1$$ i.e. $$\rho^2 + z^2/4 = 1$$ where $$\rho$$ is the radius in the x-y plane. Now, parameterizing this is a simple task, the square of $$\rho$$ plus the square of $$z/2$$ gives 1. So set $$\rho = \sin \theta$$ and $$z/2 = \cos \theta \Rightarrow z = 2\cos \theta$$. Can you fill in the rest? (think about $$x$$ and $$y$$ in spherical coordinates)

edit: And also consider an appropriate domain for $$\theta$$ if you want the lower half of the ellipsoid.