Question

已知方程x²＋y²-2（m+3）x+2（1-4m²）y+16m²×m²

Answer 1

方程配平方,整理得：[x-(m+3)]^2+[y-(4m^2-1)]^2 = 7m^2-6m+1 ,

因为,7m^2-6m+1 > 0 恒成立,

所以,此方程表示的圆的圆心为（m+1,4m^2-1）.

对于圆心（x,y）,满足：x = m+1 ,y = 4m^2-1 ,可得：y+1 = 4(x-1)^2 ,

所以,圆心C的轨迹方程为：y = 4x^2-8x+3 .