Final answer:
The eccentricity of an ellipse is the ratio of the distance between its foci to the length of its semimajor axis. For an ellipse with foci at (0,0) and (0,8) and a major axis length of 16 units, the semimajor axis is 8 units, and the eccentricity is 1, but this describes a line rather than an ellipse, since ellipses must have an eccentricity less than 1.
Step-by-step explanation:
The question concerns the eccentricity of an ellipse with given foci and major axis length. Eccentricity (e) of an ellipse is calculated by dividing the distance (f) between the foci by the length of the semimajor axis (a). In this case, the foci are at (0,0) and (0,8), so the distance between the foci is 8 units. Given that the major axis is 16 units long, the semimajor axis is half of this, which is 8 units. As such, the eccentricity e = f/a = 8/8 = 1. However, since an ellipse is a closed curve and its eccentricity must be less than 1, there seems to be a misunderstanding in the question as presented - if the major axis is 16 units long and the distance between the foci is also 16 units, then the shape would not be an ellipse. Ellipses always have eccentricities less than 1. A correct interpretation might be that if the ellipse was intended to have a major axis of 16, then the semimajor axis would be 8, and if the foci are indeed 8 units apart, the eccentricity would be 8/8 = 1, describing a line rather than an ellipse. So the correct answer in the context of a typical ellipse should be c) Eccentricity less than 1.