Question

平面内与定点F（1,1）及定直线2X-Y-1=0的距离相等的点的轨迹是?

Answer 1

设点O(x,y)

OF=√[(x-1)^2+(y-1)^2]

O到直线2X-Y-1=0的距离d

d=│2x-y-1│/√(2*2+1*1)

OF=d

[(x-1)^2+(y-1)^2]=(2x-y-1)^2/5 整理得

x^2+4y^2+4xy-6x-12y+9=0

(x+2y-3)^2=0

x+2y-3=0 轨迹是一条直线