Question

过点P(8,1)的直线与双曲线x²－4y²=4相交于A、B两点,且P是线段AB的中点,则直线AB的方程为___________.

Answer 1

解析:设A(x₁,y₁),B(x₂,y₂),则x₁²－4y₁²=4,                                                                    ①

x₂²－4y₂²=4.                                                                                                            ②

①－②,得(x₁+x₂)(x₁－x₂)－4(y₁+y₂)(y₁－y₂)=0.

又x₁+x₂=16,y₁+y₂=2,

∴=2.

∴直线AB的方程为y－1=2(x－8).

答案:2x－y－15=0