（1）M(x0,y0),A(x1,y1),B(x2,y2)
A.B关于原点对称,x2=-x1,y2=-y1,B(-x1,-y1)
K1*K2=(y1-y0)/(x1-x0) * (-y1-y0)/(-x1-x0)
=(y1-y0)/(x1-x0) * (y1+y0)/(x1+x0)
=(y1^2-y0^2)/(x1^2-x0^2)
x1^2/a^2+y1^2/b^2=1
x0^2/a^2+y0^2/b^2=1
两式相减,(x1^2-x0^2)/a^2+(y1^2-y0^2)/b^2=0
整理得(y1^2-y0^2)/(x1^2-x0^2)=-b^2/a^2
e=√6/3,b^2=a^2-c^2=a^2-2a^2/3=a^2/3
K1*K2=-b^2/a^2=-1/3
（2）M（0,1）,即b=1,e=√6/3
,b^2=a^2-c^2=a^2-2a^2/3=a^2/3,a^2=3
,x^2/3+y^2=1
直线AB:y=kx+m
椭圆方程与y=kx+m联立
得到(1+3k^2)x^2+6kmx+3m^2-3=0
A(x1,y1),B(x2,y2)
x1+x2=-6km/(1+3k^2),x1x2=(3m^2-3)/(1+3k^2)
,k1+k2=(y1-1)/x1+(y2-1)/x2=[(y1-1)x2+(y2-1)x1]/(x1x2)
将y1=kx1+m,y2=kx2+m代入整理得
,k1+k2=2k+[(m-1)(x1+x2)/(x1x2)]
代入x1+x2,x1x2
得k1+k2=2k/(m+1)=3,m=2k/3 -1
y=kx+m=kx+2k/3 -1=k(x+2/3) -1
直线AB过定点(-2/3,-1)
Delt=(6km)^2-4(1+3k^2) (3m^2-3)>0
即3k^2>m^2-1=(2k/3 -1)^2-1
解得k>0或k