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#13ef6e1d-1d22-4894-955c-4a3fac58f74f中等解答题直线与圆的位置关系直线与圆+圆锥曲线

22.已知P(x0P(x_{0}y0)y_{0})为圆C:(xt)2+(ys)2=r2(r>0)C:(x-t)^{2}+(y-s)^{2}=r^{2}(r>0)上的任意一点,当aba\ne b时,x0y0+a+x0y0+b\vert x_{0}-y_{0}+a\vert +\vert x_{0}-y_{0}+b\vert的值与x0x_{0}y0y_{0}无关,下列结论正确的是 [ ①② ].
(1)当ab=22r\vert a-b\vert =2\sqrt{2}r时,点(t,s)(t,s)的轨迹是一条直线;
(2)当ab=22\vert a-b\vert =2\sqrt{2}时,有rr的最大值为1;
(3)当r=2r=\sqrt{2}b=2b=2时,aa的取值范围a6a\geqslant 6