Final answer:
The center of the ellipse given by the equation ((x-1)²)/100 + (y²)/16 = 1 is at (1,0). The semimajor axis of an ellipse with a major axis of 16 cm is 8 cm. With an eccentricity of 0.8, the ellipse is considered very elongated.
Step-by-step explanation:
The question asks about the center of an ellipse given by the equation ((x-1)²)/100 + (y²)/16 = 1. The center of an ellipse is the midpoint of both the major and minor axes. In the given equation, the center can be found by looking at the values with the variables in the equation. The center is at (h,k) where h and k are the values that x and y are subtracted from, respectively. Therefore, the center of this ellipse is at (1,0).
Regarding the semimajor axis and eccentricity, if the major axis is 16 cm, then the semimajor axis, which is half the length of the major axis, is 8 cm. Eccentricity is a measure of how much an ellipse deviates from being circular; it ranges from 0 to 1. An eccentricity of 0.8 suggests the ellipse is quite elongated, as it is closer to 1 than to 0.