若橢圓mx^2+my^2與直線x+y-1=0相較於A B兩點,過原點與線段AB中點的直線的斜率k為二分之根號二,則n/m=? 詳細過程答案是根號2/2

聯立mx^2+ny^2=1 x+y-1=0消去y,得（m+n)x^2-2nx+n^2-1=0A,B的橫坐標x1,x2是上面方程的解A,B中點的橫坐標是（x1+x2）/2x1+x2=2n/(m+n)A,B中點的橫坐標是n/(m+n)代入直線方程x+y-1=0A,B中點的縱坐標是m/(m+n)過原點...