Final answer:
The question is about defining the characteristics of an ellipse with a given center, major axis length, and an extreme point on the minor axis. The ellipse is horizontally oriented with a semi-major axis of 4 units and a total minor axis length of 2 units.
Step-by-step explanation:
The student's question pertains to the characteristics of an ellipse, which is a fundamental concept in mathematics, particularly in the study of conic sections. To define an ellipse, we need to know several parameters, including the center, the lengths of the major and minor axes, and the coordinates of the extreme points (vertices) along these axes.
Given that the center of the ellipse is (-4, -2), the length of the major axis is 8 units, and one extreme of the minor axis is (-3, -2), we know that the ellipse is horizontally oriented because the x-coordinate changes along the minor axis, and the y-coordinate remains constant. Since the major axis is 8 units long, the semi-major axis is half of this, which is 4 units. The minor axis length can also be inferred from the difference in the x-coordinates of the center and the given extreme of the minor axis.
The extreme point of the minor axis at (-3, -2) suggests that the minor axis is 2 units long in total since the center (-4, -2) is 1 unit away from the extreme, and the semi-minor axis is half of the minor axis.