消去y并整理得(k2?4)x2?2kx?3?0， 故x1?x2??
2k3，xx??． ····························································· 6分 12k2?4k2?4????????OA?OB，即x1x2?y1y2?0．
而y1y2?k2x1x2?k(x1?x2)?1，
33k22k2?4k2?1?2?2?1?2于是x1x2?y1y2??2． k?4k?4k?4k?4????????1所以k??时，x1x2?y1y2?0，故OA?OB． ················································ 8分
21412当k??时，x1?x2??，x1x2??．
21717?????AB?(x2?x1)2?(y2?y1)2?(1?k2)(x2?x1)2，
而(x2?x1)2?(x2?x1)2?4x1x2
424?343?13?2?4??， 1717172?????465所以AB?． ······················································································ 14分
17《数 学》答案及评分参考 第6页（共6页）