Question

点P在直线2x+y-5=0上,且点P到直线x-y-1=0的距离等于根号2,求点P的坐标

Answer 1

设P（x1,y1）,则2x1+y1-5=0,y1=5-2x1...(1)

|x1-y1-1|/√(1^2+(-1)^2)=√2 |x1-y1-1|=2.(2)

(1)代入(2)得：|x1-5+2x1-1|=2 |3x1-6|=2 3x1-6=2 x1=8/3或者 3x1-6=-2 x1=4/3

y1=-1/3或者y1=7/3

P(8/3,-1/3)或者P(4/3,7/3)