Question

multiple - choice question
what happens to eccentricity as the ellipse gets flatter, more like a parabola or line?
it increases to 1
it decreases to 0.
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Explanation:

Step1: Recall the formula for eccentricity of an ellipse

The eccentricity \(e\) of an ellipse is given by \(e=\frac{c}{a}\), where \(c\) is the distance from the center to a focus and \(a\) is the semi - major axis length, and \(0 < e<1\) for an ellipse.

Step2: Analyze the relationship between the shape of the ellipse and \(e\)

As the ellipse gets flatter (more elongated), the value of \(c\) approaches \(a\). Mathematically, \(\lim_{c
ightarrow a}e=\lim_{c
ightarrow a}\frac{c}{a} = 1\). When \(e = 1\), the conic is a parabola (in the limit as the ellipse flattens).

Answer:

It increases to 1.