Question

平面上有三个点A(-2,y),B(0,),C(x,y),若⊥,则动点C的轨迹方程是_________.

Answer 1

y²=8x

=(0,)-(-2,y)=(2,-),
=(x,y)-(0,)=(x,),
∵⊥,∴·=0,
∴(2,-)·(x,)=0,即y²=8x.
∴动点C的轨迹方程为y²=8x.