Question

图所示为圆外一点p(A,B).直线ap与圆相交a及b两点

Answer 1

a)设PD切圆C于D连接CD

由勾股定理：PD^2=PC^2-CD^2=d^2-r^2

由切割线定理:PA*PB=PD^2=d^2-r^2.

b)将d^2-r^2用坐标系中距离公式即得.

c)C1圆心(1,-1),r^2=6

C2圆心(2,1),r^2=4

由上动点轨迹:(x-1)^2+(y+1)^2-6=(x-2)^2+(y-1)^2-4

即:2x+4y-5=0

圆幂可表示为d^2-r^2这是d、r幂差的形式,所以称为圆幂