Question

已知直線l經過點P(3,1),且被兩平行直線l₁:x+y+1=0和l₂:x+y+6=0截得的線段長為5,則直線l的方程為___________.

Answer 1

x=3或y=1

解析:

設直線l與l₁、l₂分別交于A(x₁、y₁)、B(x₂、y₂).則

x₁+y₁+1=0,x₂+y₂+6=0.

兩式相減得(x₁-x₂)+(y₁-y₂)=5.①

又(x₁-x₂)²+(y₁-y₂)²=25.②

解①②得x₁-x₂=5,y₁-y₂=0或x₁-x₂=0,y₁-y₂=5.

故直線l的傾斜角為0°或90°.

答案:x=3或y=1