Answer
Option D
Work Step by Step
Given: $45y^2-200x^2=1800$
Rewrite the equation in standard form
$$\frac{y^2}{40}-\frac{x^2}{9}=1$$
The denominator of $x^2$ is smaller than $y^2$, so the transverse axis is vertical.
Identify the vertices, foci, and asymptotes. Note that $a=2\sqrt 10$ and
$b=3$. The $x^2-term$ is negative, so the transverse axis is vertical. Find the foci:
$c^2=a^2+b^2=(2\sqrt 10)^2+3^2=49\\
\rightarrow c=7$
The foci are at $(0,\pm \sqrt 7)$
Hence, the correct option is D
