清楚点.已知集合A={(x,y)丨ax+y=1},B={(x,y)丨x+ay=1},C={(x,y)丨xˇ2+yˇ2=1},试问:当a取何值时,(A∪B)∩C有两个元素集合.
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![清楚点.已知集合A={(x,y)丨ax+y=1},B={(x,y)丨x+ay=1},C={(x,y)丨xˇ2+yˇ2=1},试问:当a取何值时,(A∪B)∩C有两个元素集合.](/uploads/image/z/12152487-39-7.jpg?t=%E6%B8%85%E6%A5%9A%E7%82%B9.%E5%B7%B2%E7%9F%A5%E9%9B%86%E5%90%88A%3D%7B%28x%2Cy%29%E4%B8%A8ax%2By%3D1%7D%2CB%3D%7B%28x%2Cy%29%E4%B8%A8x%2Bay%3D1%7D%2CC%3D%7B%28x%2Cy%29%E4%B8%A8x%CB%872%2By%CB%872%3D1%7D%2C%E8%AF%95%E9%97%AE%EF%BC%9A%E5%BD%93a%E5%8F%96%E4%BD%95%E5%80%BC%E6%97%B6%2C%EF%BC%88A%E2%88%AAB%EF%BC%89%E2%88%A9C%E6%9C%89%E4%B8%A4%E4%B8%AA%E5%85%83%E7%B4%A0%E9%9B%86%E5%90%88.)
清楚点.已知集合A={(x,y)丨ax+y=1},B={(x,y)丨x+ay=1},C={(x,y)丨xˇ2+yˇ2=1},试问:当a取何值时,(A∪B)∩C有两个元素集合.
清楚点.
已知集合A={(x,y)丨ax+y=1},B={(x,y)丨x+ay=1},C={(x,y)丨xˇ2+yˇ2=1},试问:当a取何值时,(A∪B)∩C有两个元素集合.
清楚点.已知集合A={(x,y)丨ax+y=1},B={(x,y)丨x+ay=1},C={(x,y)丨xˇ2+yˇ2=1},试问:当a取何值时,(A∪B)∩C有两个元素集合.
∵集合A={(x,y)|ax+y=1},B={(x,y)|x+ay=1},C={(x,y)|x2+y2=1},
∴集合A,B表示直线,C表示单位圆,
∴A∪B表示两条直线上的点,
∴(A∪B)∩C表示两条直线与圆的交点,
∴ {ax+y=1x2+y2=1解得 {x=0y=1, {x=2a1+a2y=1-2a21+a2,
或 {x+ay=1x2+y2=1解得 {x=1y=0, {x=1-a21+a2y=2a1+a2,
又∵(A∪B)∩C有两个元素,
∴两直线只能垂直,
∴a=0,故答案为0.