c^2=a^2+b^2=1+3=4,c=2
即右焦點(diǎn)坐標(biāo)是(2,0)
直線方程是y=k(x-2)
代入曲線方程:x^2-[k(x-3)]^2/3=1
3x^2-k^2(x^2-6x+9)=3
(3-k^2)x^2+6k^2x-9k^2-3=0
x1+x2=6k^2/(k^2-3)
x1x2=-3(3k^2+1)/(3-k^2)
y1y2=k^2(x1-2)(x2-2)=k^2[x1x2-2(x1+x2)+4]
把上面的代入進(jìn)去.
然后根據(jù)OA⊥OB,則有x1x2+y1y2=0
代入計(jì)算就得出k了.