设：O(0,0),A(a,0),P(acost,bsint),t≠0
OP⊥AP--->(acost,bsint)•(acost-a,bsint) = 0
　　　　即 a²(cos²t-cost)+b²sin²t
　　　　= a²cos²t-a²cost+(a²-c²)sin²t
　　　　= a²-a²cost-c²(1-cos²t)
　　　　= c²cos²t-a²cost+(a²-c²)=0
--->e²cos²t-cost+(1-e²)=0
--->(cost-1)[e²cost-(1-e²)]=0
∵cost≠1--->-1≤cost=1/e²-1≤1--->0≤1/e²≤2
--->1/2≤e²＜1--->√2/2≤e＜1