Chapter 13 - Section 13.2 - The Ellipse and the Hyperbola - Exercise Set - Page 939: 34

It's a hyperbola

Writing in standard form $\frac{x^2}{4^2}−\frac{y^2} {2^2}=1$ Intercepts : $y=0$, $x^2=16$, $(4;0)$, $(-4;0)$ Asymptotes: $y=+/−(\frac{b}{a})x,$ $y=0.5x$ and $y=−0.5x$ The graph is as below and the $x-intercepts$ are shown