Question

已知M是x轴上一动点,一条直线经过点A(2,1)并且垂直于AM交y轴于N,过点M、N分别作两坐标轴的垂线,设它们的交点为P(x,y),则点P的轨迹方程是(    )

A.2x-y-3=0          B.2x+y-5=0          C.x-2y=0             D.x+2y-4=0

Answer 1

B

解:∵P(x,y),

∴N(0,y),M(x,0).

又A(2,1),由此可得AM及AN的斜率.

由已知AM⊥AN,∴k_AM·k_AN=-1,即得P点轨迹方程为2x+y-5=0.