设方程x눀+y눀-2(m+3)x-2(1--4m)y+16m四次方+9=0若该方程表示一个圆,求m

2025-04-02 09:36:12
推荐回答(1个)
回答1:

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