过点A（4,0）作直线L交圆O：x^2+y^2=4于B,C两点,求线段BC中点P的轨迹方程.
问题描述：
过点A（4,0）作直线L交圆O：x^2+y^2=4于B,C两点,求线段BC中点P的轨迹方程.
答
设B(x1,y1),C(x2,y2),BC中点为M(x0,y0),则x1²+y1²=4,x2²+y2²=4以上两式相减,得(x1+x2)(x1-x2)+(y1-y2)(y1+y2)=0又x0=(x1+x2)/2,y0=(y1+y2)/2∴(y1-y2)/(x1-x2)=-(x1+x2)/(y1+y2)=-x0/y0,即k=-x0...