若椭圆
|
依题意可知抛物线的焦点为M(b,0),椭圆的焦点为F2(
,0),F1(-a2-b2
,0)a2-b2
∵|
|=2|F1M
|,F2M
∴
=2F1M
或F2M
=-2F1M
,F2M
①当
=2F1M
时,F2M
∴
+b=2(b-a2-b2
),整理得9a2=10b2,a2-b2
∴e=
=c a
=a 2-b2 a
;10 10
②当
=-2F1M
时,F2M
∴
+b=-2(b-a2-b2
),整理得a2=10b2,a2-b2
∴e=
=c a
=a 2-b2 a
;3 10 10
则此椭圆的离心率为
或10 10
.3 10 10
故答案为:
或10 10 3 10 10