Question 1170467
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From the condition, the major semi-axis is vertical and the distance between the foci is  2 - (-6) = 8.


Therefore, the eccentricity  "e"  is half of this distance, i.e.  e = 8/2 = 4.


Let the foci be the points F1 and F2, and let V be the vertex of the ellipse closest to F1.


Then the distance from  F1  to  V  is (a-e),  while the distance from F2 to V is (a+e), where "a" is the major semi-axis.


The sum of these distances is equal to 14, according to the condition

    (a-e) + (a+e) = 14,


which implies

    2a = 14,  a = 7.


Thus the major semi-axis is a = 7 and the eccentricity is 4.


Then  from  c = {{{sqrt(a^2 - b^2)}}},  we have for the minor semi-axis "b"

    {{{c^2}}} = {{{a^2 - b^2}}},

    {{{b^2}}} = {{{a^2 - c^2}}} = {{{7^2 - 4^2}}} = 49 - 16 = 33.


The center of the ellipse is at  (-3,-2);  therefore, its equation is


    {{{(x+3)^2/33}}} + {{{(y+2)^2/49}}} = 1.
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Solved.