0)的离心率为根号2/2其中左焦点F(-20)(1)求椭圆C的方程（2）若直线y=x+m与椭圆C交于

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离心率e=c/a,c=2,2/a=√2/2,a=2√2,b^2=a^2-c^2=4,
设A（x1,y1),B(x2,y2),
椭圆方程为：x^2/8+y^2/4=1,
y=x+m,代入椭圆方程,
x^2/8+(x+m)^2/4=1,
3x^2+4mx+2m^2-8=0,
根据韦达定理,
x1+x2=-4m/3,
设M（x0,y0),x0=(x1+x2)/2=-2m/3,
y0=-2m/3+m=m/3,
M关于y=x+1的对称点是(m/3-1,-2m/3+1),在圆x^2+y^2=1上,
(m/3-1)^2+(-2m/3+1)^2=1,
m^2/9-2m/3+1+4m^2/9-4m/3+1=1
5m^2/9-2m+1=0
5m^2-18m+9=0
(5m-3)(m-3)=0
∴m=3/5或3
======以下答案可供参考======
供参考答案1:
离心率e=c/a,c=2,2/a=√2/2，a=2√2，b^2=a^2-c^2=4,
设A（x1,y1),B(x2,y2),
椭圆方程为：x^2/8+y^2/4=1,
y=x+m,代入椭圆方程，
x^2/8+(x+m)^2/4=1,
3x^2+4mx+2m^2-8=0,
根据韦达定理，
x1+x2=-4m/3,
设M（x0,y0),x0=(x1+x2)/2=-2m/3,
y0=-2m/3+m=m/3,
M关于y=x+1的对称点是(m/3-1,-2m/3+1),在圆x^2+y^2=1上,
(m/3-1)^2+(-2m/3+1)^2=1,
m^2/9-2m/3+1+4m^2/9-4m/3+1=1
5m^2/9-2m+1=0
5m^2-18m+9=0
(5m-3)(m-3)=0
∴m=3/5或3