28.在平面直角坐標(biāo)系xOy中,⊙O的半徑為1,M為⊙O上一點(diǎn),點(diǎn)N(0,-2).
對于點(diǎn)P給出如下定義:將點(diǎn)P繞點(diǎn)M順時針旋轉(zhuǎn)90°,得到點(diǎn)P′,點(diǎn)P′關(guān)于點(diǎn)N的對稱點(diǎn)為Q,稱點(diǎn)Q為點(diǎn)P關(guān)于點(diǎn)M,N的“中旋點(diǎn)”.
(1)如圖1,已知點(diǎn)P(4,0),點(diǎn)Q為點(diǎn)P關(guān)于點(diǎn)M,N的“中旋點(diǎn)”.
①若點(diǎn)M(0,1),在圖中畫出點(diǎn)Q,并直接寫出OQ的長度為
;
②當(dāng)點(diǎn)M在⊙O上運(yùn)動時,直線y=x+b上存在點(diǎn)P關(guān)于點(diǎn)M,N的“中旋點(diǎn)”Q,求b的取值范圍;
(2)點(diǎn)P(t,0),當(dāng)點(diǎn)M在⊙O上運(yùn)動時,若⊙O上存在點(diǎn)P關(guān)于點(diǎn)M,N的“中旋點(diǎn)”Q,直接寫出t的取值范圍.