SOLUTION: Find the equation of the ellipse with the following properties. The ellipse with foci at (4, 0) and (-4, 0); y-intercepts (0, 3) and (0, -3).

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the equation of the ellipse with the following properties. The ellipse with foci at (4, 0) and (-4, 0); y-intercepts (0, 3) and (0, -3).       Log On


   

Question 717120: Find the equation of the ellipse with the following properties.
The ellipse with foci at (4, 0) and (-4, 0); y-intercepts (0, 3) and (0, -3).

Answer by solver91311(24713) About Me  (Show Source):
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The foci are on the axis and symmetrical to the origin, hence the center of the ellipse is at .

The foci of an ellipse centered at the origin with a horizontal major axis are at . The -intercepts of such an ellipse are at the endpoints of the minor axis, . We need to find the -coordinates of the endpoints of the major axis, . Fortunately we know that , , and are related by:



Plugging in the values we know:



Solve for then use the values of and to derive the equation of an ellipse centered at the orgin with a horizontal major axis:



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