已知圆c过点p(1,1),且与圆M(x+2)²+（y+2)²=r²(r＞0)关于直线x+y+2=0对称

1.两圆对称,则半径相同(=r)
M(-2,-2)
直线x+y+2=0,y = -x - 2的斜率为-1,MC的斜率为1
MC的方程:y + 2 = 1(x + 2),y = x
两直线的交点为A(-1,-1)
A为的MC中点,设C(a,b):
-1 = (a -2)/2,a = 0
-1 = (b -2)/2,b = 0
圆C的方程:x² + y²= r²
代入P(1,1),r² = 2
圆C的方程:x² + y²= 2
2.Q(m,n)
m² + n² =2
PQ = (m-1,n-1)
MQ = (m+2,n+2)
向量PQ*向量MQ = (m-1)(m+2) + (n-1)(n+2)
= m² + n² + m + n -4
= 2 + m + n - 4
= m + n -2
= m -√(2-m²) -2 (n= √(2-m²)时,向量PQ*向量MQ较大)
易知m = -√(2-m²) = -1时,向量PQ*向量MQ最小,为-4