The angular momentum of a planet is conserved if taken with respect to:

Question

a)The center of the ellipse

b) The focus of the ellipse at the sun

c)The focus of the ellipse opposite the sun

d)Both foci of the ellipse

Answer 1

Hmmm. None of the answers are correct, as the focus of the ellipse is not at the center of the Sun. Consider Jupiter and the Sun. The Baricenter is one solar diameter from the center of the Sun, and both jupiter and the Sun rotate in an ellipse about that baricenter.

Now for Sun and smaller planets, the Sun is very close to the foci of the ellipse.

a) is a bad answer
b. is nearly right

Now, the real problem is that the system has to have conservation of angular momentum, and as discussed above, the Sun is also moving about the baricenter. The sum of the planet's angular momentum plus the angular momentum of the Sun about the Baricenter is then conserved.

So if one blithely assumes The sun's center is the foci (baricenter) , then its angular momentum is zero.
so, if the Sun has zero angular momentum, what about c)?
it would be true in that case, the angular momentum about the other foci would be conserved, however if the Sun is in however in a slight elliptical orbit, then c) is not true, as that the remote foci is not a point of rotational symettry of the system.

d) answed above.

So what does your teacher want as a "correct" answer. I would go with b), however, it is not a good question, and I would not argue with the teacher on this, because it depends on assumtions, "foci at the sun" is the main problem. In real systems, it the center of rotation (foci, or baricenter), is never at the center of one body in a two body system.
http://en.wikipedia.org/wiki/Barycentric_coordinates_%28astronomy%29#Two-body_problem