Sketching a level curve

When I had to sketch level curves, my teacher showed me a nice and easy to understand method:
Your equation is f(x,y) = x^2 + 2y^2 . Write it as z = x^2+2y^2
which could also be re-written as z=(x^2/1)+(y^2/1/2)

Now that you have a clearer idea of what this could represent : if z=k a constant then for a certain z you have an ellipse of k=(x^2/1)+(y^2/1/2)
Sketch it for some values and then connect the elements together. Since z can't be negative (x and y are both squared) it will be something like a parabola going up in the z-dir. So I guess it is a paraboloid, where each "slice" taken in z=k plane is an ellipse given by k=(x^2/1)+(y^2/1/2).