Question

Endpoints of major axis at (0,6) and (0,-6) endpoints of minor axis at (-3,0) and (3,0)

Answer 1

We can see that the center is (0,0)

and from commments we know tat it is ellipse

since major axis is y direction ( and center (0,0)), it is a vertical ellipse
in form
$\frac{x^{2}}{b^{2}} + \frac{y^{2}}{a^{2}} =1$

where a is the distance from the center to major axis end
b is distance of minor axis
and a>b always for ellipse

from (0,0) to (0,6) is 6 units, major axis
from (0,0) to (3,0) is 3 units, minor axis

$\frac{x^{2}}{3^{2}} + \frac{y^{2}}{6^{2}} =1$