Question

過點P(8,1)的直線與雙曲線x²－4y²=4相交于A、B兩點,且P是線段AB的中點,則直線AB的方程為___________.

Answer 1

解析:設A(x₁,y₁),B(x₂,y₂),則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.

∴直線AB的方程為y－1=2(x－8).

答案:2x－y－15=0