As the given vertices are at a distance of 12 units:
As the major axis is vertical you have the next generall equation:
[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1[/tex]
To find the center (h,k) of the ellipse use the coordinates of that vertices as follow:
[tex](\frac{0+0}{2},\frac{6-6}{2})=(0,0)[/tex]
Now use the distance between those vertices to find a:
[tex]a=\frac{12}{2}=6[/tex]
b is the distance of minor axis divided into 2:
[tex]b=\frac{4}{2}=2[/tex]
Then, you get the next equation for the given ellipse:
[tex]\begin{gathered} \frac{(x-0)^2}{2^2}+\frac{(y-0)^2}{6^2}=1 \\ \\ \frac{x^2}{4}+\frac{y^2}{36}=1 \end{gathered}[/tex]
