求过定点(0,1)的直线被双曲线x^2-(y^2)/4=1 截得的弦中点轨迹方程

求过定点(0,1)的直线被双曲线x^2-(y^2)/4=1 截得的弦中点轨迹方程
求过定点(0,1)的直线被双曲线x^2-(y^2)/4=1 截得的弦中点轨迹方程

求过定点(0,1)的直线被双曲线x^2-(y^2)/4=1 截得的弦中点轨迹方程
弦A(x1,y1)B(x2,y2)
弦中点P(x,y)
x1+x2=2x
y1+y2=2y
(y1-y2)/(x1-x2)=(y-1)/(x-0)
x1^2-(y1^2)/4=1
x2^2-(y2^2)/4=1两个式子相减
(x1-x2)(x1+x2)-(y1-y2)(y2+y1)/4=0
(x1+x2)-(y1+y2)(y1-y2)/4(x1-x2)=0
2x-2y(y-1)/4x=0
4x^2-y(y-1)=0
弦中点轨迹方程4x^2-y(y-1)=0