Question

已知双曲线方程为x2/9-y2/12＝1.动直线l经过点G（2,2）与双曲线交于不同的两点M,N.是否存在直线l,使G平

Answer 1

k(L)=(yM-yN)/(xM-xN)=(y-2)/(x-2)

xM+xN=yM+yN=2*2=4

[(xM)^2/9-(yM)^2/12]-[(xN)^2/9-(yN)^2/12]=1-1

12*(xM+xN)*(xM-xN)-9*(yM+yN)*(yM-yN)=0

12*4-9*4*(yM-yN)/(xM-xN)=0

4-3*(y-2)/(x-2)=0

L:4x-3y-2=0