Relationship between Focal Points and Eccentricity

The distance between the focal points is also related to the eccentricity (and hence the ratio of the semi-major and semi-minor axes).

In fact, if you take how far the focal points are from the centre (called the focal distance or c) and divide by the semi-major axis a, you get the eccentricity e.

When the focal points are on the same spot (c = 0), the eccentricity is zero and we have a circle. Most planet orbits are, as we'll see, close to zero eccentricity.