So the trajectory equation of the center of gravity c is y = 4-x.
2、OC^2=m^2+(4-m)^2
? =2m^2-8m+ 16
? =2(m^2-4m+8)
? =2(m-2)^2+8
So OC is the smallest when m=2.
So the general equation of circle C is (x-2) 2+(y-2) 2 = 2.
4 concise methods. .
c 1:x2+y2-4x+2y = 1 1
c2:x2+y2+2x-6y=- 1
C 1-c2: -6x+8y= 12
Simplification: y=3/2+3/4x