∴焦点坐标F(1,0),准线方程x=-1.
过P,Q分别作准线的射影分别为A,B,
则由抛物线的定义可知:|PA|=|PF|,|QF|=|BQ|,
∵|PF|=3|QF|,
∴|AP|=3|QB|,
即|BN|=3|AN|,
∴P,Q的纵坐标满足yP=3yQ,
设P(
| y2 |
| 4 |
则Q(
| y2 |
| 36 |
| y |
| 3 |
则N(-1,0),
∵N,Q,P三点共线,
∴
| y | ||
|
| ||
|
解得y2=12,
∴y=±2
| 3 |
此时x=
| y2 |
| 4 |
| 12 |
| 4 |
即点P坐标为(3,±2
| 3 |
故答案为:(3,±2
| 3 |
| y2 |
| 4 |
| y2 |
| 36 |
| y |
| 3 |
| y | ||
|
| ||
|
| 3 |
| y2 |
| 4 |
| 12 |
| 4 |
| 3 |
| 3 |