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[x-(m+3)]^2+[y+(1-4m^2)]^2=(m+3)^2+(1-4m^2)^2-16m^4-9
[x-(m+3)]^2+[y+(1-4m^2)]^2=-7m^2+6m+1
表示一个圆
所以-7m^2+6m+1>0
7m^2-6m-1<0
(7m+1)(m-1)<0
-1/7<m<1

r^2=-7m^2+6m+1=-7(m-3/7)^2+16/7
-1/7<m<1
所以m=-3/7,r^2最大=16/7
m=-1/7或1，r^2=0
边界取不到
所以0<r<4√7/7

圆心[(m+3),-(1-4m^2)]
x=m+3,y=-(1-4m^2)
m=x-3
y=4m^2-1=4(x-3)^2-1
y=4x^2-24x+35

X^2+Y^2-2(m+3)X+2(1-4m^2)Y+16m^4+9=0
(X-(m+3))^2+(Y+1-4m^2)^2=(m+3)^2+(1-4m^2)^2-9-16m^4
等式左边可以化为
左=(m+3)^2+(1-4m^2)^2-9-16m^4
=m^2+6m+9+1-8m^2+16m^4-9-16m^4
=-7m^2+6m+1

1.
左=-(7m+1)(m-1)>0
=> -1/7<m<1

2.
圆的标准方程为(x-a)^2+(y-b)^2=r^2
那么等式右边配方后左边部分应该是半径的平方
要求左边一元二次部分的取值范围要配方，如下
R^2=左=-7(m-3/7)^2+16/7<=16/7
=> 0<R<=4*7^0.5/7 (7^0.5表示根号7)

3.
圆心为(m+3,4m^2-1)
y=4m^2-1
=4*((m+3)^2-6m-9)-1
=4*(m+3