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Numerade Educator

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Problem 29 Hard Difficulty

Sketch and identify a quadric surface that could have the traces shown.

Traces in $ x = k $
Traces in $ y = k $

Answer

Circular paraboloid

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Video Transcript

So when we have X being constant so X equals K. Um, or depending on how we write it, uh, we see that the form of the equation Um What? Just call it a constant. We end up getting a Z squared equals a y r sorry z squared plus a y equals B When we let y be constant, we get X squared plus z squared equals R squared. And therefore the equation of the surface is somehow of the form X squared plus a y plus z squared equals r squared, then substituting Why eagles one We just get that X squared plus z squared, um equals zero. And what that ultimately means is that a is going to be equal to r squared. So now what we have is x squared plus r squared y plus z squared equals r squared. Then what we can do is we know that when X is equal to plus or minus two, the parabola passes through the origin. So that way we know that R squared is equal to four. So now we have X squared plus four y plus z squared equals for and this is going to be the equation of a circular Prabha, Lloyd. Um, and the way that we can draw that is, if this is our Z or X and or y What we'll have is a circular Prabal oId that somehow faces this direction and kind of comes up here. So we see it like this, and that would be our circular probable Lloyd that faces this direction.