若方程x²+y²-2x+2my+2m²-6m+9=0表示圆,则m范围是?当半径最大时,圆的方程为?
问题描述:
若方程x²+y²-2x+2my+2m²-6m+9=0表示圆,则m范围是?当半径最大时,圆的方程为?
答
x²+y²-2x+2my+2m²-6m+9=0
x²-2x+1+y²+2my+m²+m²-6m+9-1=0
(x-1)²+(y+m)²+m²-6m+8=0
(x-1)²+(y+m)²=-(m²-6m+8)
(x-1)²+(y+m)²=-(m²-6m+9)+1
(x-1)²+(y+m)²=1-(m-3)²
1-(m-3)²>=0
(m-3)²-1