Question

点F(a,0)(a>0),点P 在Y轴上运动,M在X轴上,N为动点,且向量PF乘以向量PM =0,向量PN+向量PM=0

Answer 1

设M(X1,0),P(0,Y1),N(X,Y)

向量PF乘以向量PM =（a,-Y1）(X1,-Y1)=0

则aX1+Y1^2=0

向量PN+向量PM=(X,Y-Y1)+(X1,-Y1)=(X+X1,Y-2Y1)=0

则X+X1=0 X1=-X

Y-2Y1=0 Y1=Y/2

则a(-X)+(Y/2)^2=0

Y^2=4aX

即N的轨迹方程为 Y^2-4aX=0