and
and with a major axis of length 26.
We must interpret the information given to us in the above problem. First, we see that the foci are 10 units apart (and live on the y-axis). Thus, we have
Moreover,
since the length of the major axis is 26. Since the center of the ellipse
is at 
, the vertices of the ellipse
must be at 
and
.
(Question: How do we know that the vertices are not
and
?) Finally, we just need to find out
the value of b. From the relationship
we know that
This can be simplified to
Thus we see that
Now we can write the standard equation of the ellipse. It is
Before moving on, note that the eccentricity of this ellipse is
which is approximately 0.3846. Because this number is “fairly small”, we should expect that the ellipse in question is not much different from a circle.
For a quick look at this ellipse, see FIGURE E6.
James A. Sellers