1.
解方程组 =>两个交点 (-1,3)(-6,-2)
设圆心(x,y) x-y-4=0 =>y=x-4
圆心到两点距离相等
(x+1)^2+(x-4-3)^2=(x+6)^2+(x-4+2)^2
=>x=1/2,y=x-4=-7/2
方程为
(x-1/2)^2+(y+7/2)^2=(-1-1/2)^2+(3+7/2)^2=89/2
2.A 显然在直线x+y=1上,所以A为切点.所以,圆心在过A点垂直于直线x+y=1的直线和直线y=-2x的交点上.
过A点垂直于直线x+y=1的直线斜率=（-1）/（-1）=1
方程y+1=(x-2) =>y=x-3
y=x-3与y=-2x交点 (1,-2)
圆方程：
(x-1)^2+(y+2)^2=(2-1)^2+(-1+2)^2=2
B(2,-2.5) 圆心O(1,-2) OB斜率=(-2+2.5)/(1-2)=-1/2
所求弦斜率=(-1)/(-1/2)=2
弦方程:(y+2.5)=2(x-2) =>y=2x-6.5