6 设集合A={(x,y)/x2+y2≤4},B={(x,y)/(x-1)2+(y-1)2≤r2}A∩B=B,r的范围
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6 设集合A={(x,y)/x2+y2≤4},B={(x,y)/(x-1)2+(y-1)2≤r2}A∩B=B,r的范围
![6 设集合A={(x,y)/x2+y2≤4},B={(x,y)/(x-1)2+(y-1)2≤r2}A∩B=B,r的范围](/uploads/image/z/18553393-1-3.jpg?t=6+%E8%AE%BE%E9%9B%86%E5%90%88A%3D%EF%BD%9B%EF%BC%88x%2Cy%EF%BC%89%2Fx2%2By2%E2%89%A44%EF%BD%9D%2CB%3D%EF%BD%9B%EF%BC%88x%2Cy%EF%BC%89%2F%28x-1%292%2B%28y-1%292%E2%89%A4r2%EF%BD%9DA%E2%88%A9B%3DB%2Cr%E7%9A%84%E8%8C%83%E5%9B%B4)
A表示的是以原点为圆心,半径为2的圆内所有点,B则是以(1,1)为圆心,半径为r的圆内所有点.A∩B=B,即B属于A.解题如下:
因为A∩B=B,所以B属于A,即
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因为A∩B=B,所以B属于A,即
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