# Thread: Describe the level surfaces of the function

1. ## Describe the level surfaces of the function

f(x,y,z)= x^2+ 3y^2+ 5z^2

k=x^2+ 3y^2+ 5z^2 if k=0 we have a ellipsewith with origin 0,0
when k>0 family of ellipses of one sheet
K<0 family of ellipses

I do not know if I am doing it right or if I am describing them exactly.

2. Originally Posted by andreaspohle
f(x,y,z)= x^2+ 3y^2+ 5z^2

k=x^2+ 3y^2+ 5z^2 if k=0 we have a ellipsewith with origin 0,0
when k>0 family of ellipses of one sheet
K<0 family of ellipses

I do not know if I am doing it right or if I am describing them exactly.
If $k > 0$, then ellipsoid's, if $k = 0$, just one point at the origin and nothing for $k< 0$ .