C:x^2+y^2-2x-2y+1=0 => (x-1)^2 + (y-1)^2 =1
圆心 (1,1),半径 R=1.圆与y轴相切于(0,1),与x轴相切于(1,0).
1.当b=1时,M(0,1),MP垂直MQ,=> PQ是圆的直径
=》 PQ在直线 y=x 上,k=1
2.k>3,y=kx 与圆的交点满足：(x-1)^2 + (kx-1)^1=1
(k^2+1) x^2 - 2(1+k) x +1 = 0
=> x1,x2 = [1+k ±√(2k)] /(k^2+1),x1+x2 = 2(1+k)/(k^2+1),x1* x2 = 1/(k^2+1)
MP垂直MQ => [ (b - k * x1) /(-x1)] * [ (b - k * x2) /(-x2)] = -1
=> (b - k * x1) * (b - k * x2) = - x1 * x2
=> b^2 - k(x1+x2) * b + (k^2+1) x1* x2 = 0
=> b^2 - 2k(1+k)/(k^2+1) * b + 1 =0
=> b1,b2 = .= [ k(k+1) ± √ ( 2k^3 - k^2 -1) ] / (k^2+1)