Question

过抛物线Y^2=2PX的焦点F作倾斜角为135°的直线,交抛物线于A,B两点,则OAB的面积为：

Answer 1

抛物线y^2=2px(p>0) 焦点F（p/2,0）

k=-1

直线程

y=-x+p/2 x=-y+p/2

y^2=2px

消x

y^2=-2py+p^2

整理 y^2+2py-p^2=0

y1y2=-p^2 y1+y2=-2p

|y1-y2|=根号[(y1+y2)^2-4y1y2]

=根号[4p^2+4p^2]

=4根号2p

S△OAB=S△OFA+S△OFB

=1/2*|y1-y2|*OF

=1/2*4根号2p*p/2

=根号2p^2