设集合M={(x,y)|x^2+y^2=4},N={(x,y)|(x-1)^2+(y-1)^2=r^2}(r＞0),当M∩N=空集_数学解答

设集合M={(x,y)|x^2+y^2=4},N={(x,y)|(x-1)^2+(y-1)^2=r^2}(r＞0),当M∩N=空集时,求实数r的取值范围

人气：211 ℃　时间：2020-04-22 07:29:21

解答

M={(x,y)|x^2+y^2=4},N={(x,y)|(x-1)^2+(y-1)^2=r^2}(r＞0)M∩N= øC:(x-1)^2+(y-1)^2=r^2:circle ,center C(1,1),radius = rC1:x^2+y^2=4circle,center C1 (0,0),radius = 2CC1 = √(1+1) = √2M∩N= ø...