Question

as the foci of an ellipse become closer together.
a the ellipse becomes more like a circle.
b the ellipse becomes more eccentric.

Explanation:

Step1: Recall the property of eccentricity in ellipse

The eccentricity \(e=\frac{c}{a}\) (\(c\) is the distance from the center to a focus, \(a\) is the semi - major axis length). When the foci get closer together, \(c\) decreases.

Step2: Analyze the change of eccentricity

Since \(e = \frac{c}{a}\) and \(a>0\) (fixed for a given ellipse in this context of foci movement), as \(c\) decreases, \(e=\frac{c}{a}\) decreases.

Step3: Relate eccentricity to the shape of the ellipse

If \(e = 0\), the ellipse is a circle (\(c = 0\), foci coincide). As \(e\) increases from \(0\) to \(1\), the ellipse becomes more eccentric. Since our \(e\) is decreasing (because \(c\) is decreasing as foci get closer), the ellipse becomes more like a circle.

Answer:

A. The ellipse becomes more like a circle.