1）设圆心为C（a,b),半径为r,则圆方程为(x-a)^2+(y-b)^2=r^2
a-2b=2
a^2+(4-b)^2=r^2
(4-a)^2+(6-b)^2=r^2=> 4(4-2a)+(10-2b)*2=0 =>2a+b=9
=>5b=5=>b=1
=>a=2+2b=2+2*1=4 =>r^2=16+9=25
∴圆的标准方程(x-4)^2+(y-1)^2=5^2

2)C(4,1)到直线的距离 d=|15*4+8*1+0|/√(15^2+8^2)=4
∴弦长L=2√(r^2-d^2)=2*√(25-16)=2*3=6