已知:方程x²+y²-2﹙m+3﹚x+2(1-4m²)y+16m^4+9=0表示一个圆 求该圆半径r的取值范围
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![已知:方程x²+y²-2﹙m+3﹚x+2(1-4m²)y+16m^4+9=0表示一个圆 求该圆半径r的取值范围](/uploads/image/z/3001514-50-4.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BC%9A%E6%96%B9%E7%A8%8Bx%26%23178%3B%EF%BC%8By%26%23178%3B%EF%BC%8D2%EF%B9%99m%EF%BC%8B3%EF%B9%9Ax%EF%BC%8B2%281-4m%26%23178%3B%29y%2B16m%5E4%2B9%3D0%E8%A1%A8%E7%A4%BA%E4%B8%80%E4%B8%AA%E5%9C%86+%E6%B1%82%E8%AF%A5%E5%9C%86%E5%8D%8A%E5%BE%84r%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
已知:方程x²+y²-2﹙m+3﹚x+2(1-4m²)y+16m^4+9=0表示一个圆 求该圆半径r的取值范围
已知:方程x²+y²-2﹙m+3﹚x+2(1-4m²)y+16m^4+9=0表示一个圆 求该圆半径r的取值范围
已知:方程x²+y²-2﹙m+3﹚x+2(1-4m²)y+16m^4+9=0表示一个圆 求该圆半径r的取值范围
x²+y²-2﹙m+3﹚x+2(1-4m²)y+16m^4+9=0
∴ x²-2(m+3)x+(m+3)²+y²+2(1-4m²)y+(1-4m²)²=-16m^4-9+(m+3)²++(1-4m²)²
∴ [x-(m+3)]²+[y+(1-4m²)]²=-16m^4-9+m²+6m+9+1-8m²+16m^4
∴ [x-(m+3)]²+[y+(1-4m²)]²=-7m²+6m+1
∴ r²=-7m²+6m+1=-7(m-3/7)²+16/7
∴ 0
方程可变为(x-(m+3))²+(y+(1-4m²))²+16m^4+9-(m+3)²-(1-4m²)²=0
(x-(m+3))²+(y+(1-4m²))²=-(7m+1)(m-1),若圆存在,则-(7m+1)(m-1)>0即(7m+1)(m-1)<0 -(1/7)<m<1
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方程可变为(x-(m+3))²+(y+(1-4m²))²+16m^4+9-(m+3)²-(1-4m²)²=0
(x-(m+3))²+(y+(1-4m²))²=-(7m+1)(m-1),若圆存在,则-(7m+1)(m-1)>0即(7m+1)(m-1)<0 -(1/7)<m<1
r²=-7m²+6m+1=-7(m-3/7)²+16/7 (m-3/7)²大于等于0,0
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圆变形为 [x-(m+3)]²+[y+(1-4m²)]²=-7m²+6m+1=r²
∴ r²=-7(m-3/7)²+16/7
∴ 0