Question

已知动点P在曲线2x2-y=0上移动,则点A(0,-1)与点P连线中点的轨迹方程...

已知动点P在曲线2x2-y=0上移动,则点A(0,-1)与点P连线中点的轨迹方程是______.

Answer 1

设点A(0,-1)与点P连线中点坐标为(x,y),则由中点坐标公式可得P(2x,2y+1),
∵动点P在曲线2x2-y=0上移动,
∴2(2x)2-(2y+1)=0
即8x2-2y-1=0
故答案为:8x2-2y-1=0.