已知椭圆X^2/（a^2）+Y^2/（a^2-1）=1(a>1)的左右焦点F1、F2,抛物线C:y^2=2px,以F2为

(1)椭圆X^2/（a^2）+Y^2/（a^2-1）=1(a>1)
半焦距c=a^2-(a^2-1)=1
F1(-1,0),F2(1,0)
抛物线C:y^2=2px,以F2为焦点,
p/2=1,p=2,
y^2=4x
直线F1M:y=k(x+1),
直线F1M与抛物线c相切,
即方程联立后delt=0
方程联立得ky^2-4y+4k=0
delt=0,k=1 或k=-1
规定M在X轴上方
k=1,解得y=2,x=1,
所以M（1,2）,N（1,-2）
(2)M在椭圆上,根据椭圆定义
MF1+MF2=2a
MF1^2=(1+1)^2+2^2=8
MF2^2=0^2+2^2=4
2a=2√2+2,a=√2+1
b^2=a^2-c^2=(√2+1)^2-1=2√2+2
椭圆方程x^2/(3+2√2)+y^2/(2+2√2)=1
e=c/a=1/(√2+1)=√2-1

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