已知两条直线a1x+b1y+1=0和a2x+b2y+1=0都过点A(1,2),求过两点P1(a1,b1),P2(a2,b2)的直线的方程
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![已知两条直线a1x+b1y+1=0和a2x+b2y+1=0都过点A(1,2),求过两点P1(a1,b1),P2(a2,b2)的直线的方程](/uploads/image/z/2540179-19-9.jpg?t=%E5%B7%B2%E7%9F%A5%E4%B8%A4%E6%9D%A1%E7%9B%B4%E7%BA%BFa1x%2Bb1y%2B1%3D0%E5%92%8Ca2x%2Bb2y%2B1%3D0%E9%83%BD%E8%BF%87%E7%82%B9A%281%2C2%29%2C%E6%B1%82%E8%BF%87%E4%B8%A4%E7%82%B9P1%28a1%2Cb1%29%2CP2%28a2%2Cb2%29%E7%9A%84%E7%9B%B4%E7%BA%BF%E7%9A%84%E6%96%B9%E7%A8%8B)
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已知两条直线a1x+b1y+1=0和a2x+b2y+1=0都过点A(1,2),求过两点P1(a1,b1),P2(a2,b2)的直线的方程
已知两条直线a1x+b1y+1=0和a2x+b2y+1=0都过点A(1,2),求过两点P1(a1,b1),P2(a2,b2)的直线的方程
已知两条直线a1x+b1y+1=0和a2x+b2y+1=0都过点A(1,2),求过两点P1(a1,b1),P2(a2,b2)的直线的方程
把A(1,2)坐标代入,两条直线的方程 a1x+b1y+1=0和a2x+b2y+1=0得
a1+2b1+1=0
a2+2b2+1=0
a1-a2+2(b1-b2)=0
a1-a2=2(b2-b1)
过P1(a1,b1),P2(a2,b2)的直线的方程:
(y-b1)/(b2-b1)=(x-a1)/(a2-a1)
-2(y-b1)=x-a1
x+2y-(a1+2b1)=0
∵a1+2b1+1=0
a1+2b1=-1
∴所求直线方程为 :x+2y+1=0