ANSWER
C, D, and E
EXPLANATION
The given ellipse has been translated therefore the center is no longer at the origin.
Option A is not correct.
The major axis is the horizontal axis. Its length is 8 units.
Option B is also not correct.
The vertices are where the major horizontal axis intersected the ellipse. They are indeed 4 units to the right and left of the center.
Option C is correct.
The foci can be found using
[tex] {a}^{2} - {b}^{2} = {c}^{2} [/tex]
a=4 is the distance from the center to the vertex and b=2 is the distance from the center to the co-vertex.
[tex] {4}^{2} - {2}^{2} = {c}^{2} [/tex]
[tex]16 - 4 = {c}^{2} [/tex]
[tex]12 = {c}^{2} [/tex]
[tex]c = \pm \sqrt{12} [/tex]
[tex]c = \pm 2\sqrt{3} [/tex]
Option D is also correct.
The directrices are parallel to the semi-minor axis therefore they are vertical lines.
Option E is also correct.
