解设A(x0,y0),M(x,y)则AM=(x-x0,y-y0)MB=(4-x,-2-y)由向量AM=2向量MB,知(x-x0,y-y0)=2(4-x,-2-y)即x-x0=8-2xy-y0=-4-2y即x0=3x-8y0=3y+4又由点A在圆x^2+y^2=4上则x0^2+y0^2=4即(3x-8)^2+(3y+4)^2=4故圆的方程为9x^2+...