1.x^2+y^2-2(t+3)x+2(1-4t^2)y+16t^4+9=0,
配方得[x-(t+3)]^2+[y+1-4t^2]^2=(t+3)^2+(1-4t^2)^2-16t^4-9
=1+6t-7t^2=-7(t-3/7)^2+16/7,(1)
当t=3/7时圆的面积最大,这时圆的方程为
（x-24/7)^2+(y+13/49)^2=16/7.
2.点P（3,4t^2)恒在所给的圆内,
代入（1）得t^2+1