| ||
4 |
x22 |
4 |
∵y=
1 |
4 |
∴y′=
1 |
2 |
∴切线MQ的斜率为:kMQ=
x1 |
2 |
∴MQ的方程为y-
x12 |
4 |
x1 |
2 |
∴x12-2x1x+4y=0.(8分)
∵MQ过Q(x0,-1),
∴x12-2x1x0-4=0,
同理x22-2x2x0-4=0,
∴x1,x2为方程x2-2xx0-4=0的两个根,
∴x1x2=-4.(10分)
又kMN=
| ||||
x2−x1 |
x1+x2 |
4 |
∴MN的方程为y-
x12 |
4 |
x1+x2 |
4 |
∴y=
x1+x2 |
4 |
所以直线MN过点(0,1).(12分)
1 |
4 |
x | 2 |
| ||
4 |
x22 |
4 |
1 |
4 |
1 |
2 |
x1 |
2 |
x12 |
4 |
x1 |
2 |
| ||||
x2−x1 |
x1+x2 |
4 |
x12 |
4 |
x1+x2 |
4 |
x1+x2 |
4 |