题目

若双曲线E：－y2＝1(a>0)的离心率等于，直线y＝kx－1与双曲线E的右支交于A，B两点． (1)求k的取值范围； (2)若|AB|＝6，点C是双曲线上一点，且，求k，m的值． 答案：(1)由 故双曲线E的方程为x2－y2＝1. 设A(x1，y1)，B(x2，y2)， 由 得(1－k2)x2＋2kx－2＝0.① ∵直线与双曲线右支交于A，B两点， 所以1<k<. 整理得28k4－55k2＋25＝0， ∴k2＝或k2＝. 又1<k<，∴k＝， 所以x1＋x2＝4， y1＋y2＝k(x1＋x2)－2＝8. 设C(x3，y3)，由得， (x3，y3)＝m(x1＋x2，y1＋y2) ＝(4m,8m)．∴x3＝4m，y3＝8m. (选用适当的介词填空) from...to ,between,in,of,behind, to,at,on,with,over(1) Our teacher asks us to keep our hands __________ our backs. (2) Tina lives __________ Room 206，the second floor __________ that building. (3) My friends often come and stay __________ me. (4) The hospital is next __________ the shop. (5) Would you like to come to my house __________ my birthday. (6) We usually go to school __________ Monday __________ Friday. (7) There is a small bridge __________ the liver. (8) The post office is __________ the left of the hospital. (9) You can come here __________ 8:00 tomorrow. (10) Jane sits __________ Nancy and me.