Question

As an ellipse becomes more eccentric, the following occurs to the shape and the distance between the foci:

a) The shape becomes more circular, and the distance between the foci decreases.
b) The shape becomes more circular, and the distance between the foci increases.
c) The shape becomes more elongated, and the distance between the foci decreases.
d) The shape becomes more elongated, and the distance between the foci increases.

Answer 1

The shape of an ellipse becomes more elongated, and the distance between the foci increases as the eccentricity increases.

Step-by-step explanation:

As an ellipse becomes more eccentric, the shape becomes more elongated, and the distance between the foci increases. Therefore, the correct answer is d) The shape becomes more elongated, and the distance between the foci increases. An ellipse is a closed curve such that the sum of the distances from a point on the curve to the two foci is a constant, and as the eccentricity increases, the foci are spaced further apart and the shape deviates more from a circle, leading to greater elongation.