Eccentricity of the Ellipse

In summary, To find the eccentricity of an ellipse, use the formula e = c/a, where c^2 = a^2 - b^2 and the standard form of an ellipse is x^2/a^2 + y^2/b^2 = 1. If you do not have a formula or a textbook, you can search for one online.
  • #1
TonyC
86
0
How would I find the eccentricity of the ellipse:
x^2/49 + y^2/64 = 1

:confused:
 
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  • #2
The standard form of an ellipse is [tex]\frac{{x^2 }}{{a^2 }} + \frac{{y^2 }}{{b^2 }} = 1[/tex].

Another constant c is defined as: [itex]c^2 \equiv a^2 - b^2[/itex]

Finally, we define the eccentricity as: [itex]e = \frac{c}{a}[/itex]
 
  • #3
Do you know a formula for eccentricity? I would be very surprized if your textbook asks a question like this and does not include a formula!

If your textbook does not have such a formula or you do not have a textbook (not a good idea!) you could go to "google.com" and enter "ellipse eccentricity". I just did that and found a very simple formula at the first hit.
 
  • #4
Thank you very much
 

What is the eccentricity of an ellipse?

The eccentricity of an ellipse is a measure of how elongated or elongated the ellipse is. It is represented by the letter "e" and is calculated by dividing the distance between the foci by the length of the major axis.

What is the range of values for eccentricity?

The range of values for eccentricity is between 0 and 1, where 0 represents a circle and 1 represents a line.

What does an eccentricity of 0.5 indicate?

An eccentricity of 0.5 indicates that the ellipse is halfway between a circle and a line. It means that the distance between the foci is half the length of the major axis.

How does eccentricity affect the shape of an ellipse?

The eccentricity affects the shape of an ellipse by determining how elongated or flattened it is. The closer the eccentricity is to 0, the more circular the ellipse will be. The closer it is to 1, the more elongated or flattened the ellipse will be.

What is the relationship between eccentricity and the motion of planets?

The eccentricity of a planet's orbit determines the shape of its elliptical path around the sun. A lower eccentricity means a more circular orbit, while a higher eccentricity means a more elongated orbit. This can affect the planet's speed and distance from the sun during different points in its orbit.

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