Question 1088643: The center of an ellipse is on (-2, -1) and one of its vertex is on (3, -1). It the length of each latus rectum is 4, find the equation of the ellipse, its excentricity and the coordinates of its foci.
Answer by MathLover1(20850)   (Show Source):
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 is an ellipse with center ( , ), horizontal axis length  , and vertical axis length  ,vertices are at ( ±  ,), foci is at ( ±  , )
Note that the center is the midpoint of the segment joining the foci.
if the center of an ellipse is on ( ,  ), we have  and 
vertices are at ( ± , )=( , )
=>
=>
foci is at ( ± , )= ( ± , )
so far, your equation is:
the length of each latus rectum is: 
 => => =>
foci is at:
( ±  , )=>the coordinates of its foci
(  , ) or (  , )
your equation is:
 =>the equation of the ellipse
and, its eccentricity:  ≈ 
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