Question

What is the eccentricity of an infinitely long ellipse?

Answer 1

1

Step-by-step explanation:

Given
`a`, half the length of the major axis, and
`b`, half the length of the minor axis for an ellipse, its eccentricity is
`\displaystyle e=\sqrt{1-(b^2)/(a^2)}`, which tells us how close the ellipse is to the shape of a circle or how flat and round it is. An infinitely long ellipse would have an infinitely long major axis, so the greater the
`a` value, the eccentricity gets infinitely closer to 1.

Answer 2

The eccentricity of an infinitely long ellipse would theoretically approach 1, as eccentricity measures the degree of elongation. The formula to calculate it is e = f/a, where f is the distance to a focus and a is half the major axis. However, an infinitely elongated ellipse would no longer be a true ellipse as it stretches towards infinity.

Step-by-step explanation:

The question of what the eccentricity of an infinitely long ellipse is can be answered by understanding how eccentricity is defined. The eccentricity (e) of an ellipse is the measure of its elongation and is calculated by dividing the distance from the center of the ellipse to one of its foci (f) by half the length of the major axis (a), using the formula e = f/a. For a 'normal' ellipse, this value ranges from 0 (a perfect circle) to just under 1 (a very elongated ellipse).

In the case of an infinitely long ellipse, essentially this would represent an ellipse with an infinite major axis. This hypothetical scenario would imply that the ellipse becomes more and more elongated, stretching towards infinity. As the length of the major axis grows without bounds, theoretically, the eccentricity approaches 1, which is the maximum value for an ellipse before it becomes a parabola. However, once it becomes infinitely long, it no longer retains the closed curve nature of an ellipse.