已知两条直线L1:aX-bY+4=0,L2:(a-1)x+y+b=0.求分别满足下列条件的a和b的值.(1)求直线L1过点(-...已知两条直线L1:aX-bY+4=0,L2:(a-1)x+y+b=0.求分别满足下列条件的a和b的值.(1)求直线L1过点(-3,-1),
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 12:48:49
![已知两条直线L1:aX-bY+4=0,L2:(a-1)x+y+b=0.求分别满足下列条件的a和b的值.(1)求直线L1过点(-...已知两条直线L1:aX-bY+4=0,L2:(a-1)x+y+b=0.求分别满足下列条件的a和b的值.(1)求直线L1过点(-3,-1),](/uploads/image/z/8568369-9-9.jpg?t=%E5%B7%B2%E7%9F%A5%E4%B8%A4%E6%9D%A1%E7%9B%B4%E7%BA%BFL1%3AaX%EF%BC%8DbY%2B4%3D0%2CL2%EF%BC%9A%28a%EF%BC%8D1%29x%2By%2Bb%3D0.%E6%B1%82%E5%88%86%E5%88%AB%E6%BB%A1%E8%B6%B3%E4%B8%8B%E5%88%97%E6%9D%A1%E4%BB%B6%E7%9A%84a%E5%92%8Cb%E7%9A%84%E5%80%BC.%281%29%E6%B1%82%E7%9B%B4%E7%BA%BFL1%E8%BF%87%E7%82%B9%28%EF%BC%8D...%E5%B7%B2%E7%9F%A5%E4%B8%A4%E6%9D%A1%E7%9B%B4%E7%BA%BFL1%3AaX%EF%BC%8DbY%2B4%3D0%2CL2%EF%BC%9A%28a%EF%BC%8D1%29x%2By%2Bb%3D0.%E6%B1%82%E5%88%86%E5%88%AB%E6%BB%A1%E8%B6%B3%E4%B8%8B%E5%88%97%E6%9D%A1%E4%BB%B6%E7%9A%84a%E5%92%8Cb%E7%9A%84%E5%80%BC.%281%29%E6%B1%82%E7%9B%B4%E7%BA%BFL1%E8%BF%87%E7%82%B9%28%EF%BC%8D3%2C%EF%BC%8D1%29%2C)
үcĹmvޡlJ已知两条直线L1:aX-bY+4=0,L2:(a-1)x+y+b=0.求分别满足下列条件的a和b的值.(1)求直线L1过点(-...已知两条直线L1:aX-bY+4=0,L2:(a-1)x+y+b=0.求分别满足下列条件的a和b的值.(1)求直线L1过点(-3,-1),
已知两条直线L1:aX-bY+4=0,L2:(a-1)x+y+b=0.求分别满足下列条件的a和b的值.(1)求直线L1过点(-...
已知两条直线L1:aX-bY+4=0,L2:(a-1)x+y+b=0.求分别满足下列条件的a和b的值.
(1)求直线L1过点(-3,-1),并且直线L1与直线L2垂直;
(2)直线L1与L2平行,并且坐标原点到L1、L2的距离相等.已知两条直线L1:aX-bY+4=0,L2:(a-1)x+y+b=0.求分别满足下列条件的a和b的值.(1)求直线L1过点(-...已知两条直线L1:aX-bY+4=0,L2:(a-1)x+y+b=0.求分别满足下列条件的a和b的值.(1)求直线L1过点(-3,-1),
(1)
∵直线L1过点(-3,-1)
∴-3a+b+4=0 ---------①
∵直线L1与直线L2
∴a(a-1)-b=0 ----------②
①②消去b得:
-3a+a²-a+4=0
a²-4a+4=0
∴a=2,b=2
(2)
∵直线L1与L2平行,且L2斜率存在为1-a
∴L1斜率也存在 为a/b
将方程写成斜截式:
L1:y=a/b*x+4/b
L2:y=(1-a)x-b
∴1-a=a/b ----------③
∵坐标原点到L1、L2的距离相等
∴纵截距互为相反数
∴4/b=b ∴b²=4,b=±2
b=2时,代入③ a=2/3
b=-2时,代入③a=2
∴符合条件的a和b的值为
a=2,b=-2或a=2/3,b=2