Sample Problem

Find the standard form of the equation of the ellipse with a center (-1, -4); vertex (-1, 3) and minor axis of length 4.


Because the minor axis has length 4, 2b=4 and b=2. Also, we know the distance from the center to one of the vertices is 7 units, a=7. Since the center and vertex share the same x-coordinate, we know the major axis is vertical. Therefore the equation of the ellipse is