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Mathematical focal length problem
Let the half focal length be c, the long semi-axis be a and the short semi-axis be b,

Then: c/a= 1/3

2c+a = 10;

The solution is a=6 and c=2.

Eccentricity is also equal to (a-b)/(a+b) =1/3;

So b = 3;;

So the standard equation of ellipse is x 2/36+y 2/9 =1.