Final answer:
The eccentricity of an ellipse decreases as it shape becomes more circular, due to the ratio of the distance between the foci to the length of the major axis approaching zero.
Step-by-step explanation:
The eccentricity of an ellipse will decrease if its shape becomes more circular. This is because the eccentricity is a measure of how much the ellipse deviates from being a circle. When the foci of an ellipse are closer together, the shape of the ellipse is closer to a circle and the eccentricity approaches 0. Conversely, as the foci move apart, the ellipse becomes more elongated and the eccentricity increases, reaching up to a maximum of 1.0 when the ellipse is extremely elongated or 'flat'.