Question

已知圆A:x^2+y^2+4x+2y-13=0,若圆B平分圆A的周长且圆B的圆心在l:y=3x上,求满足上述条件的半径最

Answer 1

圆A:x^2+y^2+4x+2y-13=0,

设圆B的方程为(x-m)^2+(y-3m)^2=r^2,

相减得（4+2m）x+(2+6m)y=13+10m^2-r^2,①

点（-2,-1）在①上,

化简得r^2=10(m+1/2)^2+41/2,

所求圆B的方程为

(x+1/2)^2+(y+3/2)^2=41/2.