Question

設(shè)過點(diǎn)P(x，y)的直線分別與x軸的正半軸和y軸的正半軸交于A、B兩點(diǎn)，點(diǎn)Q與點(diǎn)P關(guān)于y軸對稱，O為坐標(biāo)原點(diǎn)，若,且·=1,則P點(diǎn)的軌跡方程是(    )

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：設(shè)P(x,y),則Q(-x,y).設(shè)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