Answer
It is a hyperbola.
See Graph I for the graphing of the equation.
Work Step by Step
For $y^2 = x^2 + 16$, it can be rewritten as
$y^2 = x^2 + 16$
$y^2 - x^2 = 16$
$\frac{y^2}{16} - \frac{x^2}{16} = \frac{16}{16}$
$\frac{y^2}{4^2} - \frac{x^2}{4^2} = 1$
It is in the form of a hyperbola with center at (0, 0) and $y-intercepts$ at $\pm4$.
See Graph I for the graphing of the equation.