x-y+3=0,
——》y=x+3,代入圆的方程,整理得:
x^2-(a-1)x+(a^2-3)/2=0,
——》x1+x2=a-1,x1*x2=(a^2-3)/2,
——》(x1-x2)^2=(x1+x2)^2-4x1x2=7-2a-a^2,
——》(y1-y2)^2=[(x1+3)-(x2+3)]^2=(x1-x2)^2,
——》弦长2√3=√[(x1-x2)^2+(y1-y2)^2]=√(14-4a-2a^2),
——》a^2+2a-1=0,
——》a=-1+-√2.
x-y+3=0,
——》y=x+3,代入圆的方程,整理得:
x^2-(a-1)x+(a^2-3)/2=0,
——》x1+x2=a-1,x1*x2=(a^2-3)/2,
——》(x1-x2)^2=(x1+x2)^2-4x1x2=7-2a-a^2,
——》(y1-y2)^2=[(x1+3)-(x2+3)]^2=(x1-x2)^2,
——》弦长2√3=√[(x1-x2)^2+(y1-y2)^2]=√(14-4a-2a^2),
——》a^2+2a-1=0,
——》a=-1+-√2.