The projection of the intersection point on the X axis is the two focal points of the ellipse (+/-c, 0),

The slope of the straight line is 2/2 of the root sign, that is, the inclination angle is 45 degrees.

So the abscissa and ordinate of the intersection point are equal, that is, x = y = c；;

B = a-c, substitute into ellipse:

c^/a^+c^/(a^-c^)= 1，

E=c/a substitution, simplified as:

e^4-3e^2+ 1=0，

Because 0

e^=(3-√5)/2，

Prescription, e=(√5- 1)/2.