Question

若圓C與圓(x+2)²+(y-1)²=1關(guān)于原點(diǎn)對(duì)稱，則圓C的方程是(　　)

A.(x-2)²+(y+1)²=1

B.(x-2)²+(y-1)²=1

C.(x-1)²+(y+2)²=1

D.(x+1)²+(y-2)²=1

Answer 1

A

解析:

圓(x+2)²+(y-1)²=1的圓心坐標(biāo)是(-2,1),它關(guān)于原點(diǎn)的對(duì)稱點(diǎn)坐標(biāo)是(2，-1)，所以圓C的方程是(x-2)²+(y+1)²=1,或根據(jù)對(duì)稱的思想，在圓(x+2)²+(y-1)²=1中，以-x代x,以-y代y,化簡(jiǎn)整理得(x-2)²+(y+1)²=1.其實(shí)質(zhì)是求曲線方程的思想，即設(shè)圓C上任一點(diǎn)(x,y),它關(guān)于原點(diǎn)的對(duì)稱點(diǎn)(-x,-y)應(yīng)在圓(x+2)²+(y-1)²=1上，然后代入整理得(x-2)²+(y+1)²=1.