28.在平面直角坐標(biāo)系xOy中,⊙O的半徑為1,點(diǎn)A在⊙O上,點(diǎn)P在⊙O內(nèi),給出如下定義:連接AP并延長交⊙O于點(diǎn)B,若AP=kAB,則稱點(diǎn)P是點(diǎn)A關(guān)于⊙O的k倍特征點(diǎn).
(1)如圖,點(diǎn)A的坐標(biāo)為(1,0).
①若點(diǎn)P的坐標(biāo)為(-
,0),則點(diǎn)P是點(diǎn)A關(guān)于⊙O的
倍特征點(diǎn);
②在C
1(0,
),C
2(
,0),C
3(
,-
)這三個(gè)點(diǎn)中,點(diǎn)
是點(diǎn)A關(guān)于⊙O的
倍特征點(diǎn);
③直線l經(jīng)過點(diǎn)A,與y軸交于點(diǎn)D,∠DAO=60°.點(diǎn)E在直線l上,且點(diǎn)E是點(diǎn)A關(guān)于⊙O的
倍特征點(diǎn),求點(diǎn)E的坐標(biāo);
(2)若當(dāng)k取某個(gè)值時(shí),對(duì)于函數(shù)y=-x+1(0<x<1)的圖象上任意一點(diǎn)M,在⊙O上都存在點(diǎn)N,使得點(diǎn)M是點(diǎn)N關(guān)于⊙O的k倍特征點(diǎn),直接寫出k的最大值和最小值.