Graph the ellipse and find the coordinates of the center 
vertices and foci.

 = 400

equations of the form  have their center at the
origin.  So the center is (0,0)

 = 400

We want to get this either to the form

 = 1 or  = 1

The first one is shaped like an egg sitting on a table.
The second one has the shape of the number zero, like this " 0 ".
We will know which form it is in because  is always larger
than .

 = 400

Get 1 on the right by dividing through by 400:

 = 

 = 1

The larger denominator on the left side is 25,
so a² = 25, the smaller denominator of the left
is 16, so b² = 16.

So this graph is in the form  = 1

and it will have the shape of a 0.

Since a² = 25, a = 5, Since b² = 16, b = 4

The center is at the origin.

One half the major axis extends from (0,0) to (0,5),
and the other half extends from (0,0) to (0,-5).

One half the minor axis extends from (0,0) to (4,0),
and the other half extends from (0,0) to (-4,0).

So we draw an upright rectangle through those four 
points, like this:

 

Draw an upright ellipse just fitting in that rectangle,
shaped like a zero "0":



It's vetices are the "bluntest" points on the ellipse.
They are (0,5) and (0,-5)

Erase the rectangle:



Now we calculate the value of c which in the distance
from the center to the foci.  You can remember what
c is by noticing that the words "focus", "foci", and
"center" contain the letter "c".

The formula is c² = a² - b²
               c² = 25 - 16
               c² = 9
                c = 
                c = 3

So the foci are at (0,3) and (0,-3) marked below with
short lines at those points:

   

Edwin