One is based on F 1F2, and the other is based on F 1F2.

We analyze two situations separately.

1. When F 1F2 is waist, four different triangles can be drawn.

This time can be divided into two situations.

PF 1=F 1F2 or PF2=F 1F2.

①PF 1=F 1F2

At this time, PF 1=F 1F2=2c.

In an ellipse, PF 1+PF2=2a.

Then PF2=2a-2c

We know that the sum of two sides of a triangle is greater than the third side.

Then pf 1+f 1f2 >: PF2.

That is 2c+2c >；; 2a-2c

Simplified to 3c>a

Therefore, e

②PF2=F 1F2 is the same as ①, and it is still E.

2. When F 1F2 is the base, two different triangles can be drawn.

At this point, p is the endpoint of the minor axis of the ellipse.

From grade one and grade two, we can get E.

From the properties of ellipse, we know that the eccentricity of ellipse is between 0 and 1.

So 1/3

However, when e= 1/2, the point P in one coincides with the point P in two, and only two different points P can be guaranteed.

In summary, we can get the range of eccentricity: 1/3.

In addition:

I haven't slept since one o'clock, and neither has winter vacation.

Going to bed too late is not good for your health and your efficiency will be reduced.