Problem:Sketch the graph of the function, 
Notice that the level curves are ellipses. 
> with(plots):
> contourplot(2*x^2+y^2,x=4..4,y=4..4,contours=[1,2,3],scaling=CONSTRAINED);

Notice that the level curves can be written as, 
> 2*x^2+y^2 = c^2;
2 2 2 2 x + y = c
from where we can write, 
> (x/(c/sqrt(2)))^2 + (y/c)^2 = 1;
2 2 x y 2  +  = 1 2 2 c c
and this is the equation of an ellipse with semi axis, 
> a = c/sqrt(2); b = c;
1/2 a = 1/2 c 2 b = c
These ellipses grow with increasing z so the surface is, 
> plot3d(2*x^2+y^2,x=4..4,y=4..4);
