(1) 若直線y=kx+1與雙曲線3x^2-y^2=1相交于A,B兩點(diǎn),求k的范圍.(2) 在(1)條件下,問k為何值時(shí),以AB為直徑的圓過坐標(biāo)原點(diǎn)?

熱心網(wǎng)友

1)把y=kx+1代入3x^2-y^2=1 得到(3-k^2)x^2-2kx-2=0......(*)其△=4k^2+8(3-k^2)=4(3-k^2)0----√3k(OA)*k(OB)=-1---y1/x1*y2/x2=-1---x1x2+y1y2=0----2/(3-k^2)+1=0---k^2=5---k=+'-√5.所以,此圓經(jīng)過原點(diǎn)時(shí)的k值是+'-√5.