已知抛物线Y方=2PX（P>0）的焦点为F,过点F做直线L与抛物线交AB两点,抛物线的准线与X轴交于点C.证明,

Question

已知抛物线Y方=2PX（P>0）的焦点为F,过点F做直线L与抛物线交 A B两点,抛物线的准线与X轴交于点C.证明,

Answer 1

y^2=2pxF(p/2,0)过F弦AB ：y=k(x-p/2),A(x1,y1) B(x2,y2) (x1>x2)k^2(x-p/2)^2=2pxl^2x^2-(pk^2+2p)x+p^2k^2/4=0x1+x2=(pk^2+2p)/k^2=p+2p/k^2x1x2=(p^2k^2/4) /k^2=p^2/4C(-p/2,0)tanACF=y1/(x1+p/2)=k(x1-p/2)/(x1...