已知点A(6,-4),B(1,2)、C(x,y),O为坐标原点.若OC=OA+λOB(λ∈R),则点C的轨迹方程是(  ) A.2x-y+16=0 B.2x-y-16=0 C.x-y+10=0 D.x-y-10=0

问题描述:

已知点A(6,-4),B(1,2)、C(x,y),O为坐标原点.若

OC
OA
OB
(λ∈R),则点C的轨迹方程是(  )
A. 2x-y+16=0
B. 2x-y-16=0
C. x-y+10=0
D. x-y-10=0

OC
OA
OB
(λ∈R),
∴(x,y)=(6,-4)+λ(1,2),
∴x=6+λ,y=-4+2λ,
消去λ,得到y=2x-16,
点C的轨迹方程是:2x-y-16=0.
故选B.