Final answer:
Yes, the angle bisector of the angle formed by the two foci of an ellipse would intersect the major axis at the center of the ellipse, regardless of the ellipse's eccentricity. The semimajor axis is half the length of the major axis, and an eccentricity of 0.8 indicates a highly elongated ellipse.
Step-by-step explanation:
The question is whether the angle bisector of the angle formed by the two foci of an ellipse would intersect the major axis. The answer to this question is yes, it would. This is because the major axis of an ellipse is the longest diameter and it passes through both foci of the ellipse. By definition, the angle bisector divides the angle formed by the two foci into two equal angles. Since the major axis of the ellipse is the line that goes through both foci and the center of the ellipse, the angle bisector would, by necessity, intersect the major axis at the center of the ellipse, regardless of the ellipse's eccentricity.
If the major axis of an ellipse is 16 cm, the semimajor axis would be half of this length, which is 8 cm. Given the information that the eccentricity is 0.8, one can infer that this ellipse is quite elongated, as an eccentricity of 1 would denote a parabola, and an eccentricity of 0 would denote a circle. Thus, an eccentricity of 0.8 suggests an ellipse that is significantly stretched along the major axis.