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The eccentricity of an ellipse, e, is the ratio of the distance between the foci to the length of the semi-major axis. As e increases from 0 to 1, the ellipse changes from a circle (e = 0) to form a more flat shape until, at e = 1, it is effectively a straight line.

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How does the numerical value of e change as the shape of the ellipse approaches a straight line?

The numerical value of the eccentricity ( e ) of an ellipse measures how much it deviates from being circular, ranging from 0 (a circle) to just under 1 (a straight line). As the shape of the ellipse becomes more elongated, approaching a straight line, ( e ) increases and approaches 1. In the limit, as the ellipse becomes a straight line, its eccentricity reaches 1, indicating maximum elongation. Thus, the value of ( e \ continuously increases from 0 to 1 as the ellipse transforms into a straight line.


How does the numerical value of eccentricity change as the shape of the ellipse approaches a straight line?

As the shape of an ellipse approaches a straight line, its eccentricity increases and approaches 1. Eccentricity (e) is defined as the ratio of the distance between the foci and the length of the major axis; for a circle, it is 0, and for a line, it becomes 1. Thus, as an ellipse becomes more elongated and closer to a straight line, the numerical value of its eccentricity rises from 0 to nearly 1.


How does the numerical value of eccentricity change as the ellipse approaches a straight line?

As the shape of an ellipse becomes more elongated, its eccentricity, which measures the deviation from being a perfect circle, increases. Eccentricity values range from 0 (a perfect circle) to 1 (a parabola). As the ellipse approaches a straight line, its eccentricity approaches 1, indicating a greater degree of elongation and deviation from circularity. Thus, the closer the ellipse is to resembling a straight line, the closer its eccentricity gets to 1.


How does the numerical value of e change as the shape if the ellipse approaches a straight line?

As the shape of an ellipse approaches a straight line, its eccentricity ( e ) increases towards 1. The eccentricity ( e ) is defined as ( e = \sqrt{1 - \frac{b^2}{a^2}} ), where ( a ) is the semi-major axis and ( b ) is the semi-minor axis. As the ellipse becomes flatter (with ( b ) approaching 0), the ratio ( \frac{b^2}{a^2} ) approaches 0, causing ( e ) to approach 1. Thus, in this limit, the ellipse becomes a degenerate case of a straight line.


How does numerical value of e change as shape of ellipse approaches straight line?

"e" will get greater. The eccentricity for a line is one and for a circle is zero. Since it is getting closer to becoming a line it will go up in value. ; ) "e" will get greater. The eccentricity for a line is one and for a circle is zero. Since it is getting closer to becoming a line it will go up in value. ; )


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