求过定点（0,1）的直线被双曲线x²-y²/4=1截得的弦长中点轨迹方程

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
弦中点的轨迹方程是
4x^2-y(y-1)=0