Final answer:
The given information is not sufficient to determine the eccentricity, type of conic section, directrix, vertices, center, foci, or minor axis length of the conic section.
Step-by-step explanation:
a. The eccentricity of a conic section can be determined by the formula e = c/a, where c is the distance between the center and one of the foci, and a is the length of the semi-major axis. In this case, the length of semi-major axis is 4 and there is no information given about the distance between center and foci. So, we cannot determine eccentricity using the given information.
b. The type of conic section can be determined by the eccentricity value. If the eccentricity is between 0 and 1, it is an ellipse. If the eccentricity is 1, it is a parabola. If the eccentricity is greater than 1, it is a hyperbola. Since we cannot determine the eccentricity, we also cannot determine the type of conic section.
c. The directrix of a conic section depends on its type. Without knowing the type of conic section, we cannot determine the directrix either.
d. The vertices of an ellipse are the points on the major axis that are furthest from the center. Since we cannot determine the center or the type of conic section, we cannot determine the vertices.
e. The center of a conic section can be determined by finding the midpoint of the major axis. Since we do not know the major axis or the type of conic section, we cannot determine the center.
f. The foci of a conic section can be determined using the formula c² = a² - b², where a is the length of the semi-major axis and b is the length of the semi-minor axis. Since we do not know the lengths of the semi-major and semi-minor axes, we cannot determine the foci either.
g. The minor axis of an ellipse is the line segment that passes through the center and is perpendicular to the major axis. Since we cannot determine the center or the major axis, we cannot determine the minor axis length.
h. Without information about the eccentricity or any other properties of the conic section, we cannot select the correct graph.