If the center of the ellipse is at the origin (0,0) and the foci (0, ±2) lie on the major axis (which in this case is vertical), then the equation takes the form:
0) to
one of the foci (0, ±2) is c=2. Because the two vertices of the ellipse are
(0,±6), we also know that the major axis has a length of 12 [from (0, -6) to
(0, 6)], that is 2a=12 → a=6.
c2=a2-b2
(2)2=(6)2-b2
b2=32
b=√32
The equation of this ellipse is therefore
