Answer
See below
Work Step by Step
Rewrite the equation in standard form
$$\frac{x^2}{25}-\frac{y^2}{4}=1$$
If the denominator of $x^2$ is bigger than $y^2$, then the transverse axis is horizontal.
Identify the vertices, foci, and asymptotes. Note that $a=5$ and
$b=2$. The $y^2-term$ is positive, so the transverse axis is vertical and the vertices are at $(\pm 5,0)$. Find the foci:
$c^2=a^2+b^2=5^2+4^2=29\\
\rightarrow c=\sqrt 29$
The foci are at $(\pm \sqrt 29,0)$
The asymptotes are $y=\pm \frac{2}{5}$
Draw the hyperbola.
