|
∴
y1−y2 |
x1−x2 |
∵过抛物线C:y2=2px(p>0)的焦点F且斜率为1的直线l与抛物线C相交于A,B两点,
∴
y1−y2 |
x1−x2 |
p |
2 |
∵
y1+y2 |
2 |
∴y1+y2=2p,
∵y1=x1−
p |
2 |
p |
2 |
∴y1+y2=x1+x2-p,
∴x1+x2=y1+y2+p,
∵
x1+x2 |
2 |
(y1+y2+p) |
2 |
3p |
2 |
∴AB中点横坐标为
3p |
2 |
∵线段AB的中点到抛物线C准线的距离为4,
∴
p |
2 |
3p |
2 |
故选B.
|
y1−y2 |
x1−x2 |
y1−y2 |
x1−x2 |
p |
2 |
y1+y2 |
2 |
p |
2 |
p |
2 |
x1+x2 |
2 |
(y1+y2+p) |
2 |
3p |
2 |
3p |
2 |
p |
2 |
3p |
2 |