SOLUTION: Find the equation of an ellipse satisfying the given conditions. Foci: (-2,0) and (2,0); length of major axis: 8

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Question 1149938: Find the equation of an ellipse satisfying the given conditions.
Foci: (-2,0) and (2,0); length of major axis: 8
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The given foci mean the major axis is horizontal, and the center of the ellipse is at the origin, (0,0). For an ellipse with those features, the equation is

x%5E2%2Fa%5E2%2By%5E2%2Fb%5E2+=+1

a is the semi-major axis; b is the semi-minor axis.
c is the distance from the center to each focus
a, b, and c are related by the equation c%5E2+=+a%5E2%2Bb%5E2

The given information tells you a=4 and c=2; from that you can determine b and thus write the equation.