(1)若a>0,且tan角POB=1/9,
设B(m,1/m),1/9=1/m^2,a>0,m>0,m=3
y=1/3
A(1/3,1/3)
AB=3-1/3=8/3
线段AB的长为8/3
(2)在过A,B两点且顶点在直线y=x上的抛物线中,已知线段AB=8/3,试求出满足条件的抛物线的解析式
y=ax^2+bx+c
AB=8/3
设B(m,1/m),A(1/m,1/m)
(m-1/m|=8/3,3|m^2-1|=8|m|,且在它的对称轴左边时,y随着x的增大而增大,抛物线开口向下,a1
(3m+1)(m-3)=0,m=3
A(1/3,1/3),B(3,1/3)顶点C坐标C(10/6,10/6)
y=a(x-10/6)^2+10/6
1/3-10/6=a(3-10/6)^2,a=-3/4
y=-0.75*(x-5/3)^2+5/3
B) -1