In the graph above, the green line is the latus rectum, the two red
points are the foci.
The distance between the foci is given as
Since c is half the distance between foci, .
Since the latus rectum is given as 4, the y-coordinate of the
point at the top of the latus rectum is 2. So the coordinates
of the point at the top of the latus rectum are .
The equation of the ellipse is
(1)
Substituting that point:
(2)
Since and
Substituting in (2)
That has solutions a=4, a=-4, a=2, a=-2
The only one it can be is a=4
Substituting in
So the equation of the ellipse, substituting in (1),
Edwin