P is a point on the straight line x=3a/2, and the triangle F2PF 1 is an isosceles triangle with a base angle of 30 degrees.

Let m be the intersection of the straight line x=3a/2 and the X axis.

Only ∠ pf 1f2 = ∠ f 1pf2 = 30 is known.

So ∠ pf2f 1 = 60.

Then in rt delta rt delta RT△PF2M.

F2M = 1/2 * PF2 = 1/2 * 2C = c

And f2m = 3a/2-c.

So 3a/2-c=c

So 3a=4c.

e=c/a=3/4