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问题: 高分题

已知方程x^2+y^2-2(t+3)x+2(1-4t^2)y+16t^4+9=0表示一个圆.求该圆半径r的取值范围.

请高手写出详细的过程.谢谢了.

解答:

x^2-2(t+3)x+(t+3)^2+y^2+2(1-4t^2)y+(1-4t^2)^2=-16t^2-9+(t+3)^2+(1-4t^2)^2

(x-t-3)^2+(y+1-4t^2)^2=-16t^4-9+t^2+6t+9+1-8t^2+16t^4

(x-t-3)^2+(y+1-4t^2)^2=-7t^2+6t+1

-7t^2+6t+1>0
7t^2-6t-1<0
(t-1)(7t+1)<0

-1/7<t<1