例如这道题目 求与直线x-2y+1=0和2x-y+3=0距离相等的点的轨迹这里点的轨迹的意思是什么?

例如这道题目 求与直线x-2y+1=0和2x-y+3=0距离相等的点的轨迹这里点的轨迹的意思是什么?
例如这道题目
求与直线x-2y+1=0和2x-y+3=0距离相等的点的轨迹
这里点的轨迹的意思是什么?

例如这道题目 求与直线x-2y+1=0和2x-y+3=0距离相等的点的轨迹这里点的轨迹的意思是什么?
方法一：
设点的坐标是（x,y）,则这个点到两直线的距离相等,根据点到直线距离公式列方程得：
|x-2y+1|/根5=|2x-y+3|/根5
解得两个方程：
x+y+2=0;3x-3y+4=0
方法二：
设符合要求的点是(x,y)
|x-2y+1|/√5=|2x-y+3|/√5
|x-2y+1|=|2x-y+3|
所以x-2y+1=2x-y+3或x-2y+1=-(2x-y+3)
所以轨迹是两条直线
x+y+2=0
3x-3y+4=0
他们是原来直线所夹角的两条角平分线
设直线是y-1=kx
y=kx+1
L1:3x+4y-8=0与L2:3x+4y+2=0
3x+4kx+4-8=0和3x+4kx+4+2=0
x1=4/(3+4k)和x2=-6/(3+4k)
x1-x2=10/(3+4k)
y1-y2=k(x1-x2)=10k/(3+4k)
所以√[(x1-x2)^2+(y1-y2)^2]=2√2
100/(3+4k)^2+100k^2/(3+4k)^2=8
100k^2+100=128k^2+192k+72
28k^2+192k-28=0
k=1/7,k=-7
所以y=x/7+1或y=-7x+1
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是指所有满足条件的点的集合

x-2y+1=0 ，2x-y+3=0 是两条直线 这里的点的轨迹就是 所有到这两条直线的距离相等的点的集合