Question

过点Q(2,-4)做圆O:x2+y2=9的割线,交圆O于A,B求AB中点P的轨迹方程.AB中点P(x,y) 2x=xA+

Answer 1

P(x,y)

k(OP)=y/x

k(AB)=(y+4)/(x-2)

AB垂直OP,k(OP)*k(AB)=-1

(y/x)*[(y+4)/(x-2)]=-1`

(x-1)^2+(y+2)^2=5

因为P(x,y)满足题目的条件,所以就是点P的轨迹方程.