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.