Answer
It is an ellipse.
See Graph I for the graphing of the equation.
Work Step by Step
For $2x^2 + 8y^2 = 32$, it can be simplified as
$2x^2 + 8y^2 = 32$
$\frac{2x^2}{32} + \frac{8y^2}{32} = \frac{32}{32}$
$\frac{x^2}{16} + \frac{y^2}{4} = 1$
$\frac{x^2}{4^2} + \frac{y^2}{2^2} = 1$
It is an ellipse, with center at (0,0) and $x-intercept$ at $\pm4$ and $y-intercept$ at $\pm2$.
See Graph I for the graphing of the equation.