1)
x^2+y^2-2(t+3)x+2(1-4t^2)y+16t^4+9=0
[x-(t+3)]^2+[y+(1-4t^2)]^2=-7t^2+6t+1
R^2=-7t^2+6t+1
-7t^2+6t+1>0
7t^2-6t-1