Question

方程x2+y2-2(m+3)x+2(1-4m平方)y+16m四次方+9=0表示一个圆 1.求实数m的取值范围；2.该圆的半径r取值范

x2+y2-2(m+3)x+2(1-4m2)y+16m4+9=0

Answer 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<m<1

-7m²+6m+1
=-7(m²-6m/7+9/49)+16/7
=-7(m-3/7)²+16/7
∴0<r<4√7/7

追问

第二问看不懂

追答

r² =-7m²+6m+1
=-7(m²-6m/7+9/49)+16/7 配方
=-7(m-3/7)²+16/7 这个有最大值16/7 但半径是正数
∴0<r<4√7/7