SOLUTION: Find an equation of an ellipse using the following center at (2,-2) vertex at (5,-2) focus at (3,-2)

1.  Your prerequisite is the lesson
        Ellipse definition, canonical equation, characteristic points and elements 
    in this site.


2.  Notice that the center and the vertices lie in one horizontal line y = -2.


3.  The major semi-axis has the length of a = 5-2 = 3.


4.  The focal distance is 3-2 = 1.

    Hence,  = 1,  where b is the minor semi-axis length.

    Therefore,   = 1,   =  =  = 8  and b =  = .


4.  Finally, the equation of the ellipse is

     +  = 1,   or

     +  = 1.