已知圆x*x+y*y+2x-4y+1=0关于直线2ax-by+2=0(a,b属于r)对称,则ab的取值范围是?
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![已知圆x*x+y*y+2x-4y+1=0关于直线2ax-by+2=0(a,b属于r)对称,则ab的取值范围是?](/uploads/image/z/1325554-34-4.jpg?t=%E5%B7%B2%E7%9F%A5%E5%9C%86x%2Ax%2By%2Ay%2B2x-4y%2B1%3D0%E5%85%B3%E4%BA%8E%E7%9B%B4%E7%BA%BF2ax-by%2B2%3D0%28a%2Cb%E5%B1%9E%E4%BA%8Er%29%E5%AF%B9%E7%A7%B0%2C%E5%88%99ab%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%E6%98%AF%3F)
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已知圆x*x+y*y+2x-4y+1=0关于直线2ax-by+2=0(a,b属于r)对称,则ab的取值范围是?
已知圆x*x+y*y+2x-4y+1=0关于直线2ax-by+2=0(a,b属于r)对称,则ab的取值范围是?
已知圆x*x+y*y+2x-4y+1=0关于直线2ax-by+2=0(a,b属于r)对称,则ab的取值范围是?
x²+y²+2x-4y+1=0,即(x+1)²+(y-2)²=4,
∵圆关于直线对称,∴2ax-by+2=0必过圆心(-1,2).即-2a-2b+2=0,解得a+b=1
∴ab=a(1-a)=a-a²=-(a-1/2)²+1/4
故ab≤1/4
x*x+y*y+2x-4y+1=0配方一下可知圆心在(-1,2)
圆关于直线对称,显然意味着直线过圆心,既圆心坐标(-1,2)必在直线上,
代入直线方程,可得a,b满足a+b=1
均值定理可得ab<=(a+b)(a+b)/4=1/4
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