1.l:x=(y-2)/a,即y=ax+2,①
代入3x^2-y^2=1②得
3x^2-(a^2x^+4ax+4)=1,
整理得(3-a^2)x^2-4ax-5=0,③
①與②交于不同的兩點(diǎn),
∴3-a^2≠0,△/4=4a^2+5(3-a^2)=15-a^2>0,
∴a^2≠3,a^20,
由③,x1+x2=4a/(3-a^2),x1x2=-5/(3-a^2),
由①,y1y2=(ax1+2)(ax2+2)=a^2*x1x2+2a(x1+x2)+4,
由向量OA*向量OB=0得0=x1x2+y1y2=(1+a^2)x1x2+2a(x1+x2)+4,
∴-5(1+a^2)+8a^2+4(3-a^2)=0,
∴7=a^2,由x1+x2>0得a