1. ## Question on Quadric Surfaces

Hey everyone,
I am having a bit of difficulty understanding a problem. It says: The trace of the graph of z = f(x,y) = $\displaystyle \ x^2 + 2y^2$ on the plane z=3, is which of the following conic sections?

At first glance, the equation of z = $\displaystyle \ x^2 + y^2$ is an elliptic paraboloid. However, if I plug-in z=3 into the equation, I get
$\displaystyle \ x^2 + 2y^2$ = 3, which is an ellipse I believe. So, exactly how am I suppose to solve this problem. Am I already correct in assuming the answer is an ellipse? Or is my understanding of the problem incorrect.

Any help and feedback is greatly appreciated, thanks.

2. ## Re: Question on Quadric Surfaces

Here is intersection of plane z=3 with f(x,y):

3. ## Re: Question on Quadric Surfaces

^^^
Thanks man. So basically, from the 3-d graph that you presented, it appears to be an elliptic paraboloid. But with the constant z that is given, it appears to be an ellipse in the xy plane ( I believe).