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