已知：方程x²＋y²－2﹙m＋3﹚x＋2(1-4m²)y+16m^4+9=0表示一个圆 求该圆半径r的取值范围

x²＋y²－2﹙m＋3﹚x＋2(1-4m²)y+16m^4+9=0
∴ x²-2(m+3)x+(m+3)²+y²+2(1-4m²)y+(1-4m²)²=-16m^4-9+(m+3)²++(1-4m²)²
∴ [x-(m+3)]²+[y+(1-4m²)]²=-16m^4-9+m²+6m+9+1-8m²+16m^4
∴ [x-(m+3)]²+[y+(1-4m²)]²=-7m²+6m+1
∴ r²=-7m²+6m+1=-7(m-3/7)²+16/7
∴ 0