两直线l1:ax-by+b=0和l2(a-1)x+y+b=0,若l1‖l2且l1与l2的距离为根号2/2,求a,b的值

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/09 06:12:42

l1过A(0,1)
l1 // l2,a ：a-1 = -b :1,a = b - ab,a = b/(1+b)
A(0,1)与l2的距离为d = |1 + b|/√[(a-1)^2 + 1] = √2/2
(1+b)^2/√[(a-1)^2 + 1] = 1/2
2(1+b)^2 = [b/(1+b) -1]^2 +1
b = -1+√2 (a = (2-√2)/2) 或b = -1-√2 (a = (-2-√2)/2)

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