SOLUTION: 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 coo

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): You can put this solution on YOUR website!

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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