1.
O(0,0),A(1,1),B(a,0)
OA²=2
OB²=a²
AB²=(a-1)²+1
(1)OA=OB:2=a²
a=√2,B(√2,0)
a=-√2,B(-√2,0)
(2)OA=AB:2=(a-1)²+1
a=0,B(0,0)(与原点重合,舍去)
a=2,B(2,0)
(3)OB=AB:a²=(a-1)²+1
a=1,B(1,0)
2.
O(0,0),A(1,1),B(0,b)
OA²=2
OB²=b²
AB²=(b-1)²+1
(1)OA=OB:2=b²
b=√2,B(0,√2)
b=-√2,B(0,-√2)
(2)OA=AB:2=(b-1)²+1
b=0,B(0,0)(与原点重合,舍去)
b=2,B(0,2)
(3)OB=AB:b²=(b-1)²+1
b=1,B(0,1)
B∈{(-√2,0),(1,0),(√2,0),(2,0),(0,2),(0,√2),(0,1),(0,-√2)}