已知集合M={(x,y)|x²+y²≤16},N={(x,y)|(x-2)²+(y-m)²=1},若M∩N=N,则m的取值范围是?
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![已知集合M={(x,y)|x²+y²≤16},N={(x,y)|(x-2)²+(y-m)²=1},若M∩N=N,则m的取值范围是?](/uploads/image/z/2715934-22-4.jpg?t=%E5%B7%B2%E7%9F%A5%E9%9B%86%E5%90%88M%3D%7B%EF%BC%88x%2Cy%EF%BC%89%7Cx%26%23178%3B%2By%26%23178%3B%E2%89%A416%7D%2CN%3D%7B%EF%BC%88x%2Cy%EF%BC%89%7C%EF%BC%88x-2%EF%BC%89%26%23178%3B%2B%EF%BC%88y-m%EF%BC%89%26%23178%3B%3D1%7D%2C%E8%8B%A5M%E2%88%A9N%3DN%2C%E5%88%99m%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%E6%98%AF%3F)
已知集合M={(x,y)|x²+y²≤16},N={(x,y)|(x-2)²+(y-m)²=1},若M∩N=N,则m的取值范围是?
已知集合M={(x,y)|x²+y²≤16},
N={(x,y)|(x-2)²+(y-m)²=1},若M∩N=N,则m的取值范围是?
已知集合M={(x,y)|x²+y²≤16},N={(x,y)|(x-2)²+(y-m)²=1},若M∩N=N,则m的取值范围是?
M∩N=N
说明N圆内切或内含于M圆
则圆心距小于等于半径差
则
√(2^2+m^2)≤|4-1|=3
(2^2+m^2)≤9
m^2≤5
-√5≤m≤√5
∵M∩N=N,N与M内切,N的圆心在X=2上,M0N0=RM=NR=4-1=3 OM0=2,m=√(3²-2²)=±√5,∴m的取值范围是-√5≤m≤√5,