Answer
See below
Work Step by Step
Given: $49y^2-100x^2=4900$
Rewrite the equation in standard form
$$\frac{x^2}{100}-\frac{y^2}{49}=1$$
The denominator of $x^2$ is greater than $y^2$, so the transverse axis is vertical.
Identify the vertices, foci, and asymptotes. Note that $a=10$ and
$b=7$. The $x^2-term$ is negative, so the transverse axis is vertical and the vertices are at $(0,\pm 10)$. Find the foci:
$c^2=a^2+b^2=10^2+7^2=149\\
\rightarrow c=\sqrt 149$
The foci are at $(0,\pm \sqrt 149)$
The asymptotes are $y=\pm \frac{10}{7}x$
Draw the hyperbola.
