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.

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
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