Question

1. choose the best answer.

the eccentricity of an ellipse is a measure of how close an ellipse is to being ___.
center
circular
directrix
constant

Explanation:

The eccentricity \(e\) of an ellipse is calculated as \(e=\frac{c}{a}\), where \(c\) is the distance from the center to a focus and \(a\) is the distance from the center to a vertex. When \(e = 0\), \(c=0\) (the foci coincide with the center), and the ellipse is a circle (\(a = b\), since \(c^{2}=a^{2}-b^{2}\)). As \(e\) increases (approaching 1), the ellipse becomes more elongated. So, eccentricity measures how close an ellipse is to being circular.

• "Center" is a point (the mid - point of the major and minor axes of the ellipse), not a shape that the ellipse can approach in terms of eccentricity.
• A "directrix" is a line used in the definition of an ellipse (\(\text{distance from a point on the ellipse to a focus}=e\times\text{distance from the point to the directrix}\)), but it is not related to the "circularity" of the ellipse.
• "Constant" is a general term and not relevant to what the eccentricity of an ellipse measures.

Answer:

circular