Question

在圆x2+y2=9中已知点P（1,2）的动弦中点的轨迹方程是_________

Answer 1

设动弦中点坐标是A(x,y)

则A与圆心O(0,0)连线AO必垂直于AP

AP的斜率是：(y-2)/(x-1)

AO的斜率是：(y-0)/(x-0)

所以：[(y-2)/(x-1)][(y-0)/(x-0)]=-1

y(y-2)+x(x-1)=0

x²+y²-2y-x=0,此即动弦中点的轨迹方程