SOLUTION: Find an equation for the ellipse that satisfies the given conditions. Endpoints of major axis: (±9, 0), distance between foci: 8

Question 1170502: Find an equation for the ellipse that satisfies the given conditions.
Endpoints of major axis:
(±9, 0), distance between foci: 8
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The endpoints of the major axis are (-9,0) and (9,0), so the center of the ellipse is (0,0) and the semi-major axis is 9. The equation is then of the form

a is the semi-major axis and b is the semi-minor axis; a and b are related by

where c is the distance from the center to each focus.

Since the distance between the two foci is 8, the distance from the center to each focus is 4.

So , with a=9 and c=4. a^2=81; use that to determine b^2. Then plug the a^2 and b^2 numbers into the equation.

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