Question

设椭圆C:x^2/a^2+y^2/b^2=1(a>b>0)的左右焦点分别为F1,F2,点P(a,b)满足|PF2|=|F1F2|

（1）求椭圆的离心率（2）设直线PF2与圆（x+1）^2+(y-根号3)^2=16相交于M,N两点，且|MN|=5/8|AB|，求椭圆方程

Answer 1

1）|PF2|=|F1F2|√[（a-c）�0�5+b�0�5]=2ca�0�5-2ac+c�0�5+b�0�5=4c�0�5a�0�5-2ac+a�0�5-c�0�5=3c�0�5a�0�5-ac-2c�0�5=0(a-2c)(a+c)=0a=2c，c/a=1/2，离心率e=1/2 2）AB两点没说？