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Focii of an ellipse are  at  (-a e, 0)  and  ( 0, a e)

where e = eccentricity of the ellipse.    let b = semi- minor axis
 a = semi major axis. then  : 

x² / a²  + y² / b²  = 1    is the equation of  ellipse.

b² = a² ( 1 - e²)

we need to know  at least two parameters to know fully the ellipse:  a, b  or  a and e      or    b and e..   

From focii it is not possible to find exactly the semi major axis.  with the same  focii, there are infinitely many different  ellipses possible.

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