Solution: It is easy to know from the title that points F(c, 0), A(a? /c，0)。 You can set the point P(acost, bsint). (t∈R)

∵ The topic should have |PF|=|AF|, ∴ It can be obtained from the distance formula between two points:

(acost-c)？ +(bsint)？ =[(a？ /c)-c]？

Expand and arrange to obtain:

c？ Cost =c? +ac-a？ .

Divide both sides by a? , combined with e=c/a can be obtained.

e？ Cost =e? +e- 1。

∴cost=(e？ +e- 1)/e？ . And:-1≤ cost ≤ 1.

∴- 1≤(e？ +e- 1)/e？ ≤ 1.

-e？ ≤e？ +e- 1≤e？ .

∴ 1/2≤e< 1.