Question

设过点P(x，y)的直线分别与x轴的正半轴和y轴的正半轴交于A、B两点，点Q与点P关于y轴对称，O为坐标原点，若,且·=1,则P点的轨迹方程是(    )

A.3x²+y²=1(x＞0,y＞0)             B.3x²y²=1(x＞0,y＞0)

C.x²-3y²=1(x＞0,y＞0)             D.x²+3y²=1(x＞0,y＞0)

Answer 1

解析：设P(x,y),则Q(-x,y).设A(x_A),x_A,B(0,y_By_B0,=(x,y-y_B)=(x_Ax,-y).

∵=2PA,∴x=2(x_A,x),y-y_B=2y,x_A=x,y_B=3y(x＞0,y＞0).

又∵·=1,(-x,y)·(-x_A,y_B)=1,

∴(-x,y)·(x,3y)=1,

即x²+3y²=1(x＞0,y＞0).

答案：D