设椭圆方程为：x^2/a^2+y^2/b^2=1,(a>b>0),
右焦点F2（c,0),则右准线方程为：x=a/e=3a/2,
3a/2-c=4/5,
3/2-c/a=4/(5a),
3/2-e=4/(5a),
3/2-2/3=4/(5a),
25a=24,
a=24/25,
e=c/a,
2/3=c/(24/25),
c=16/25,
b=√（a^2-c^2)=8√5/25.
2b=16√5/25.
椭圆的短轴长是16√5/25.