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=2,且·=1,则点P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

答案：D如图,若P(x,y),则A(x,0),B(0,3y),

=(x,3y),

=(-x,y),

∵·=1,∴x²+3y²=1(x＞0,y＞0),即为点P的轨迹方程.