过抛物线y2=4x的焦点,且倾斜角为
|
设P(x1,y1),Q(x2,y2),则S=
|OF|•|y1-y2|.1 2
直线为x+y-1=0,即x=1-y代入y2=4x得:
y2=4(1-y),即y2+4y-4=0,∴y1+y2=-4,y1y2=-4,
∴|y1-y2|=
=(y1+y2)2-4y1y2
=416+16
,2
∴S=
|OF|•|y1-y2|=1 2
×41 2
=22
.2
故答案为:22
过抛物线y2=4x的焦点,且倾斜角为
|
设P(x1,y1),Q(x2,y2),则S=
|OF|•|y1-y2|.1 2
直线为x+y-1=0,即x=1-y代入y2=4x得:
y2=4(1-y),即y2+4y-4=0,∴y1+y2=-4,y1y2=-4,
∴|y1-y2|=
=(y1+y2)2-4y1y2
=416+16
,2
∴S=
|OF|•|y1-y2|=1 2
×41 2
=22
.2
故答案为:22