Question

问2道数学题1.已知直线l:y=ax+1与双曲线C:3x^2-y^2=1相交于A、B两点.（1）求实数a的取值范围（2）

Answer 1

1 (1)y=ax+1

x=(y-1)/a

代入3x^2-y^2=1

得3(y-1)^2/a^2-y^2=1

3(y^2-2y+1)-a^2y^2=a^2

(3-a^2)y^2-6y+3-a^2=0

要使方程有解,则需6^2-4(3-a^2)(3-a^2)>=0

(3-a^2)^2