点P(2,3)到直线:ax+(a-1)y+3=0的距离不小于3,那么a的取值范围
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![点P(2,3)到直线:ax+(a-1)y+3=0的距离不小于3,那么a的取值范围](/uploads/image/z/11608647-15-7.jpg?t=%E7%82%B9P%282%2C3%29%E5%88%B0%E7%9B%B4%E7%BA%BF%3Aax%2B%28a-1%29y%2B3%3D0%E7%9A%84%E8%B7%9D%E7%A6%BB%E4%B8%8D%E5%B0%8F%E4%BA%8E3%2C%E9%82%A3%E4%B9%88a%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
点P(2,3)到直线:ax+(a-1)y+3=0的距离不小于3,那么a的取值范围
点P(2,3)到直线:ax+(a-1)y+3=0的距离不小于3,那么a的取值范围
点P(2,3)到直线:ax+(a-1)y+3=0的距离不小于3,那么a的取值范围
d = |2a+ 3(a-1)+3|/√[a²+(a-1)²] = 5|a|/√[a²+(a-1)²] ≥ 3
25a² ≥ 9[a²+(a-1)²]
25a² ≥ 9(2a² - 2a +1)
7a² + 18a-9 ≥ 0
(7a - 3)(a+3) ≥0
a ≥ 3/7 或 a < -3
把P(2,3)代入直线:ax+(a-1)y+3=0
(2a+3a-3+3)/√(a²+a²-2a+1)≥3
25a²≥9(2a²-2a+1)
7a²+18a-9≥0
(a+3)(7a-3)≥0
解得a≥3/7或者a≤-3
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