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TA
Numerade Educator

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Problem 11 Easy Difficulty

Use traces to sketch and identify the surface.

$ x = y^2 + 4z^2 $

Answer

elliptic paraboloid

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Video Transcript

So you want to craft x equals two Y squared plus four D. Square. So fast we observed that X is always positive, no negative to be precise. And then if X equals two K, we obtained that Y squared plus four G. Is very close to K. Who is his an ellipse? Yeah, because it can be written as I squared plus Z squared divided by 1/4 equals two. Okay, so that each plane at the level of X we obtain that it is an ellipse. So how do we draw it? So the dog. So basically for the sake of convenience, let me drug, this is my ex access. This is the only stress we need. And I said this is my wife, this is my jeep. Okay so at each trace we obtained that this is this is a this is an ellipse. So this looks like something like that. So don't want support. And each point we obtained that this is an ellipse. This is an ellipse. So this isn't elliptic for a bullet.