焦點(diǎn)為F的拋物線y2=4x有三點(diǎn)ABC△ABC的重心是F|FA||FB||FC|成等差數(shù)列則直線AC

其他人氣：856 ℃時(shí)間：2020-01-27 14:43:31

優(yōu)質(zhì)解答

拋物線y^2=4x的焦點(diǎn)F為(1,0),
△ABC的重心是F,
∴xA+xB+xC=3xF=3,①
yA+yB+yC=3yF=0,
A,B,C在拋物線上,
∴|FA|=xA+1,|FB|=xB+1,|FC|=xC+1,
|FA||FB||FC|成等差數(shù)列,
<==>|FA|+|FC|=2|FB|,
<==>xA+xC=2xB,
代入①,xB=1.yB=土2,
∴xA+xC=2,yA+yC=干2.
設(shè)AC的方程是y=kx+m,代入y^2=4x,得
k^2x^2+(2km-4)x+m^2=0,
∴（4-2km)/k^2=2,
(4-2km）/k+2m=干2,
解得k=干2,m=土1,
∴AC:y=-2x+1,或y=2x-1.