Question

已知方程X^2+Y^2-2(m+3)X+2(1-4m^2)Y+16m^4+9=0表示一个圆,

Answer 1

X^2+Y^2-2(m+3)X+2(1-4m^2)Y+16m^4+9=0

(X-(m+3))^2+(Y+1-4m^2)^2=(m+3)^2+(1-4m^2)^2-9-16m^4

等式左边可以化为

左=(m+3)^2+(1-4m^2)^2-9-16m^4

=m^2+6m+9+1-8m^2+16m^4-9-16m^4

=-7m^2+6m+1

1.

左=-(7m+1)(m-1)>0

=> -1/7