Find the standard form of the equation of the ellipse (centered at the origin) with vertices (0, ±6) and foci at (0, ±2).

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.

c^{2}=a^{2}-b^{2}

(2)^{2}=(6)^{2}-b^{2}

b^{2}=32

b=√32

The equation of this ellipse is therefore