Question

一道简单的双曲线题!已知双曲线C:2x^2-y^2=2,若Q(1,1),试判断以Q为中点的弦是否存在.

Answer 1

设存在,A(x1,y1),B(x2,y2),弦的方程为为y-1=k(x-1)

2x1^2-y1^1=2

2x2^2-y2^2=2

(y2-y1)/(x2-x1)=k

(x1+x2)/2=1

(y1+y2)/2=1

(2)-(1)

2(x2-x1)(x1+x2)=(y2-y1)(y1+y2)

(y2-y1)/(x2-x1)=2(x1+x2)/(y1+y2)=2=k

y-1=2(x-1)

2x-y-1=0

2x-y-1=0

2x^2-y^2=2

-2x^2+4x-3=0

△