Question

If the eccentricity of an ellipse is 0.571 and distance between the foci of that ellipse is 3,410,000 km,
what is the length of the major axis?

5,970,000 km

6,110,000 km

5,570,000 km

5,490,000 km

What is the eccentricity of a perfect circle?

1

2

0

-1

Answer 1

To determine the length of the major axis of an ellipse when given the eccentricity and the distance between the foci, we can use the following relationships:

1. The distance between the foci \(2c\) is given as \(3,410,000\) km. Thus, we find \(c\):
\[
c = \frac{3,410,000}{2} = 1,705,000 \text{ km}
\]

2. The relationship between the semi-major axis \(a\), eccentricity \(e\), and \(c\) is given by:
\[
e = \frac{c}{a}
\]
Rearranging this gives:
\[
a = \frac{c}{e}
\]

3. Given that \(e = 0.571\), we can now calculate \(a\):
\[
a = \frac{1,705,000}{0.571} \approx 2,984,390.82 \text{ km}
\]

4. The length of the major axis \(2a\) can then be calculated as:
\[
2a \approx 2 \times 2,984,390.82 \approx 5,968,781.64 \text{ km}
\]

Rounding this to the nearest whole number gives approximately \(5,970,000\) km.

Now, for the second question regarding the eccentricity of a perfect circle:

The eccentricity of a perfect circle is:
\[
0
\]

Thus, the answers are:
- Length of the major axis: **5,970,000 km**
- Eccentricity of a perfect circle: **0**