Answer
See below
Work Step by Step
Given $$64x^2+36y^2=2304\\\frac{x^2}{36}+\frac{y^2}{64}=1$$
The denominator of $x^2$ is smaller than $y^2$, so the transverse axis is vertical.
Identify the vertices, foci, and asymptotes. Note that $a=8$ and
$b=6$. The $x^2-term$ is negative, so the transverse axis is vertical, and the vertices are at $(0,\pm 8)$.
Draw the ellipse.
