Question

已知方程x²+y²-2(m+3)x+2(1-4m²)y+16m的4次方+9=0个圆，求m得取值范围？

Answer 1

已知方程x²+y²-2(m+3)x+2(1-4m²)y+16m的4次方+9=0是个圆，求m得取值范围？
x²-2(m+3)x+(m+3)²-(m+3)²+y²+2(1-4m²)y+(1-4m²)²-(1-4m²)²+16m的4次方+9=0
[x-(m+3)]²+[y-(4m²-1)]²-m²-6m-9-1+8m²-16m的4次方+16m的4次方+9=0
[x-(m+3)]²+[y-(4m²-1)]²=-7m²+6m+1
-7m²+6m+1>0
7m²-6m-1<0
(7m+1)(m-1)<0
-1/7<m<1

Answer 2

x²+y²-2(m+3)x+2(1-4m²)y+16m^4+9=0
(x-(m+3))^2+(y+(1-4m^2))^2-(m+3)^2-(1-4m^2)^2+16m^4+9=0
(x-(m+3))^2+(y+(1-4m^2))^2=-(8m^2-6m-1)
(8m^2-6m-1)<=0
（3-根号17）/8<=m<=（3+根号17）/8

Answer 3

写成[x-(m+3)]^2+[y+(1-4m^2)]^2+m的多项式=0的形式，让m的多项式=0就好了