已知集合A={(x,y)|(x-3)^2+(y-4)^2=4/5},B={(x,y)|2|x-3|+|y-4|=入},若A∩B≠∮,则实数入的取值范围是
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![已知集合A={(x,y)|(x-3)^2+(y-4)^2=4/5},B={(x,y)|2|x-3|+|y-4|=入},若A∩B≠∮,则实数入的取值范围是](/uploads/image/z/6916245-69-5.jpg?t=%E5%B7%B2%E7%9F%A5%E9%9B%86%E5%90%88A%3D%7B%EF%BC%88x%2Cy%29%EF%BD%9C%EF%BC%88x-3%29%5E2%2B%28y-4%29%5E2%3D4%2F5%7D%2CB%3D%7B%EF%BC%88x%2Cy%29%EF%BD%9C2%EF%BD%9Cx-3%EF%BD%9C%2B%EF%BD%9Cy-4%EF%BD%9C%3D%E5%85%A5%7D%2C%E8%8B%A5A%E2%88%A9B%E2%89%A0%E2%88%AE%2C%E5%88%99%E5%AE%9E%E6%95%B0%E5%85%A5%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%E6%98%AF)
已知集合A={(x,y)|(x-3)^2+(y-4)^2=4/5},B={(x,y)|2|x-3|+|y-4|=入},若A∩B≠∮,则实数入的取值范围是
已知集合A={(x,y)|(x-3)^2+(y-4)^2=4/5},B={(x,y)|2|x-3|+|y-4|=入},若A∩B≠∮,则实数入的取值范围是
已知集合A={(x,y)|(x-3)^2+(y-4)^2=4/5},B={(x,y)|2|x-3|+|y-4|=入},若A∩B≠∮,则实数入的取值范围是
答:
集合A表示圆:(x-3)^2+(y-4)^2=4/5
x=3+2sint/√5,x-3=2sint/√5
y=4+2cost/√5,y-4=cost/√5
集合B为:2|x-3|+|y-4|=m
A∩B≠∅,说明A和B有公共解.
所以:
m=2*(2/√5)*|sint|+(2/√5)*|cost|
=(2/√5)*[2|sint|+|cost|]
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