SOLUTION: My formula is not working, please help. Elara is a moon of Jupiter. Elara’s orbit has an eccentricity of (1/5). Assume a coordinate system centered at the origin with Jupiter at

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: My formula is not working, please help. Elara is a moon of Jupiter. Elara’s orbit has an eccentricity of (1/5). Assume a coordinate system centered at the origin with Jupiter at      Log On


   

Question 736818: My formula is not working, please help.
Elara is a moon of Jupiter. Elara’s orbit has an eccentricity of (1/5). Assume a coordinate system centered at the origin with Jupiter at one of the foci on the x-axis. Find the equation for Elara’s orbit if the major axis has a length of 12 million kilometers.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
"the major axis has a length of 12 million kilometers", means that 2%2Aa=12 million kilometers.

The eccentricity given means c%2Fa=1%2F5, where c is the distance from either focus to the center of the ellipse.

Those two equations let you solve for the value of c. Once you know a and c, you can find the value of b, the length of the semi-minor axis. These have a pythagorean theorem relationship.

That should be enough for you to solve for the ellipse. If you're unsure, a further bit of work can be shown.
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Just a few minutes doing a few steps gives me the result, x%5E2%2F36%2By%5E2%2F34.56=1. We use the relationship, b%5E2=a%5E2-c%5E2.