How would one parametrise the surface:$$x^2+2y^2+z^2=1$$
I was thinking that you would need to use spherical coordinates, $x=r \sin\theta \cos\phi$, $y=r \sin\theta \sin\phi$ and $z=r\cos\theta$, although, I'm not sure how this works in regards to this specific surface because of the coefficient of the $y$-component.
Any help would be appreciated.
Thanks!
To parametrise this surface you could simply write this as : $\left ( x, y, \sqrt{1-x^2-2y^2} \right)$
This is the easiest way ! And from here you can do your Gradient or Jacobian easely. Of course there is some better way to parametrise, but you should plot and see if you can project on the (x,y) plane or something.