直线y=kx+1与双曲线3x^2-y^2=1相交于不同二点A,B

y=kx+1代人3x^2-y^2=1得：
3x^2-(kx+1)^2=1
(3-k^2)x^2-2kx-2=0
判别式△=4k^2+8(3-k^2)=-4k^2+24≥0
-√6≤k≤√6

x1+x2=2k/(3-k^2),x1x2=2/(k^2-3)
|AB|^2=(1+k^2)(x1-x2)^2
=(1+k^2)[(x1+x2)^2-4x1x2]
=(1+k^2)[4k^2/(3-k^2)^2-8/(k^2-3)]
=-4(1+k^2)(k^2-6)/(k^2-3)^2
圆心x=(x1+x2)/2=k/(3-k^2),y=kx+1=3/(3-k^2)
圆经过坐标原点
半径平方=(k^2+9)/(3-k^2)^2
所以，(1+k^2)(6-k^2)/(k^2-3)^2=(k^2+9)/(k^2-3)^2
(1+k^2)(6-k^2)=(k^2+9)
k^4-4k^2+3=0
k^2=1,或，k^2=3
因为： k^2-3≠0
所以，k^2=1

半径平方=(k^2+9)/(3-k^2)^2
=(1+9)/(3-1)^2
=10/4
=5/2
半径=√10/2

y=kx 1代人3x^2-y^2=1得：
3x^2-(kx 1)^2=1
(3-k^2)x^2-2kx-2=0
判别式△=4k^2 8(3-k^2)=-4k^2 24≥0
-√6≤k≤√6
x1 x2=2k/(3-k^2),x1x2=2/(k^2-3)
|AB|^2=(1 k^2)(x1-x2)^2
=(1 k^2)[(x1 x2)^2-4x1x2]
=(1 k^2)[4k^2/(3-k^2)^2-8/(k^2-3)]
=-4(1 k^2)(k^2-6)/(k^2-3)^2
圆心x=(x1 x2)/2=k/(3-k^2),y=kx 1=3/(3-k^2)
圆经过坐标原点
半径平方=(k^2 9)/(3-k^2)^2