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S is the surface z =√(x² + y²) and (x − 2)² + 4y² ≤ 1

I tried parametrizing it using polar coordinates setting

x = 2 + rcos(θ)But I'm not getting the ellipse that the original equation for the domain describes

y = 2rsin(θ)

0≤θ≤2π, 0≤r≤1

So far I've tried dividing everything by 4 and also tried the method of completing the square, but no success.

I'm supposed to calculate the surface area of S. But without the parametric equations, calculating the normal vector is impossible.

EDIT:Messing with the equations on Wolfram I got the following:

x = 2 + cos(u)

y = (1/2)sin(u)

0≤ u ≤2π

But when I multiply the cosine and sine by r and make r vary from 0 to 1, the parametric plot changes to something completely different

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# I Parameterize an offset ellipse and calculate the surface area

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