(Ⅰ)∵=,∴=,-----------------------------------------------------(2分) 依题意设椭圆方程为:+=1 把点(4,1)代入,得b2=5 ∴椭圆方程为+=1---------------------------------------------------(4分) (Ⅱ)把y=x+m代入椭圆方程得:5x2+8mx+4m2-20=0, 由△>0可得64m2-20(4m2-20)>0 ∴-5<m<5---------------------------------------------------(6分) (Ⅲ)设A(x1,y1),B(x2,y2),则x1+x2=-,x1x2=,-----------------------(8分) ∴kMA+kMB=+=2x1x2-(m-5)(x1+x2)-8(m-1) | (x1-4)(x2-4) | =0, ∴kMA+kMB为定值0.------------------(12分) |