Answer
Hyperbola
Work Step by Step
$16{{y}^{2}}-{{x}^{2}}=16$
Divide both sides of the equation by $16$,
$\begin{align}
& \frac{16{{y}^{2}}-{{x}^{2}}}{16}=\frac{16}{16} \\
& \frac{{{y}^{2}}}{{{1}^{2}}}-\frac{{{x}^{2}}}{{{4}^{2}}}=1
\end{align}$
Consider the standard form of the hyperbola
$\frac{{{y}^{2}}}{{{b}^{2}}}-\frac{{{x}^{2}}}{{{a}^{2}}}=1$
The simplified equation $\frac{{{y}^{2}}}{{{1}^{2}}}-\frac{{{x}^{2}}}{{{4}^{2}}}=1$ resembles the standard equation of a hyperbola.
Now, find points on the graph:
$\begin{matrix}
x & y \\
0 & -1 \\
0& 1 \\
-1 & 1 \\
1 & 1 \\
\end{matrix}$
Plot the points and connect them.
