In the ellipse to the left, the focal points have been marked. The measurement between them is always designated "a."Even when the ellipse is vertically oriented, the term "a" refers to the distance between the focal points. This is the natural outcome of the fact that only the major axis of the ellipse has focal points.
When the ratio a/b exceeds 1, the ellipse ceases to be an ellipse and becomes a hyperbola. When "a" shrinks to zero, the ratio disappears, and there is no eccentricity, meaning the ellipse becomes a perfect circle. Thus for an ellipse to exist e must always be a value less than or equal to 1, and greater than zero. 0 < e < = 1.