Answer
Ellipsoid (graph c).
Work Step by Step
Since, we have $9x^2+4y^2+2z^2=36$
This can be re-written as:
$\dfrac{9x^2}{36}+\dfrac{4y^2}{36}+\dfrac{2z^2}{36}=1$
or, $\dfrac{x^2}{2^2}+\dfrac{y^2}{(3)^2}+\dfrac{z^2}{(3 \sqrt 2)^2}=1$
The equation is a graph for an Ellipsoid as shown in graph (c).
