题目

   Watch for us on TVTHIS summer, many Beijing middle school students had a different kind of vacation. Instead of hanging out with friends or traveling, they were training hard for the National Day celebration. To mark the special anniversary (周年纪念)of China this year, the students performed a group dance in a big parade(游行)on Tian’anmen Square on October 1. Students were training from 7:30am to around 10:00am or from 4 pm to 6:30pm. It was to avoid the summer heat. They wore white hats, T-shirts and dark-blue trousers. The hats and T-shirts were printed with a red logo, the nu已知椭圆E：的左焦点F1（，0），若椭圆上存在一点D，满足以椭圆短轴为直径的圆与线段DF1相切于线段DF1的中点F。（Ⅰ）求椭圆E的方程；（Ⅱ）已知两点Q（-2，0），M（0，1）及椭圆G：，过点Q作斜率为k的直线l交椭圆G于H，K两点，设线段HK的中点为N，连结MN，试问当k为何值时，直线MN过椭圆G的顶点？（Ⅲ）过坐标原点O的直线交椭圆W：于P、A两点，其中P在第一象限，过P作x轴的垂线，垂足为C，连结AC并延长交椭圆W于B，求证：PA⊥PB。