Answer
See image:
Work Step by Step
(Graphed with geogebra)
The level curves have the form:
$k=x^{2}+9y^{2}$,
ellipses centered at the origin, with x-axis as the major axis.
The graph of $f(x, y)$ is the surface $z =x^{2}+9y^{2}$, an elliptic paraboloid.