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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.)

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  • $\begingroup$ So far all 6 posts of you have been no-clue-do-my-homework questions. See How to ask a good question. $\endgroup$
    – Saad
    Jun 17 '20 at 2:56
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$$x^2+y^2 + z^2/4 = 1$$ 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.

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