Answer
See below
Work Step by Step
Rewrite the equation in standard form
$$\frac{y^2}{196}-\frac{x^2}{100}=1$$
The denominator of $x^2$ is smaller than $y^2$, so the transverse axis is vertical.
Identify the vertices, foci, and asymptotes. Note that $a=14$ and
$b=10$. The $y^2-term$ is positive, so the transverse axis is vertical and the vertices are at $(0,\pm 14)$. Find the foci:
$c^2=a^2+b^2=12^2+10^2=296\\
\rightarrow c=2\sqrt 74$
The foci are at $(0,\pm 2\sqrt 74)$
The asymptotes are $y=\pm \frac{7}{5}x$
Draw the hyperbola.
