Question

已知圓C與圓(x-1)²+y²=1關(guān)于直線y=-x對(duì)稱(chēng)，則圓C的方程(    )

A．(x+1)2+y2=1	B．x2+y2=1
C．x2+(y+1)2=1	D．x2+(y-1)2=1

Answer 1

C

解析試題分析：(點(diǎn)軸對(duì)稱(chēng)法)由于圓關(guān)于直線對(duì)稱(chēng)，其半徑不變，只求出新的圓心即可.而關(guān)于直線y=-x對(duì)稱(chēng)，則橫、縱坐標(biāo)交換位置，并取相反數(shù).由圓(x-1)²+y²=1的圓心為(1，0)，知對(duì)稱(chēng)圓的圓心為(0，-1)，故選C.
考點(diǎn)：點(diǎn)關(guān)于直線的對(duì)稱(chēng)點(diǎn)的求法。
點(diǎn)評(píng)：點(diǎn)關(guān)于x軸的對(duì)稱(chēng)點(diǎn)為；點(diǎn)關(guān)于y軸的對(duì)稱(chēng)點(diǎn)為；點(diǎn)關(guān)于原點(diǎn)軸的對(duì)稱(chēng)點(diǎn)為；點(diǎn)關(guān)于y=x軸的對(duì)稱(chēng)點(diǎn)為；點(diǎn)關(guān)于y=-x軸的對(duì)稱(chēng)點(diǎn)為.