Question

已知双曲线X^25-Y^2 /16=1,过点p(1,1)能否作一条直线L,与双曲线交于A,B两点,且点P为线段AB的中点

Answer 1

用点差法.

设A（x1,y1),B(x2,y2),AB中点（x0,y0),x0=(x1+x2)/2,y0=(y1+y2)/2,

x1^2/25-y1^2/16=1,(1),

x2^2/25-y2^2/16=1,(2),

(1)-(2)式,

16/25-[（y1-y2)/(x1-x2)]*[(y1+y2)/2]/[(x1+x2)/2]

（y1-y2)/(x1-x2)=k,(直线斜率）,

16/25-k*y0/x0=0,

k=16/25,

∴直线方程为：(y-1)=(16/25)(x-1),

16x-25y+9=0.