已知直线Y=aX+1与双曲线3X^2-Y^2=1交于A.B两点，(1)若以AB线段为直径的圆过坐标原点，求实数a的值。(2)...

显示全部楼层 · 2011-12-13 22:14:50

OA垂直OB, (y1/x1)(y2/x2) = -1, x1x2+y1y2=0 x1x2+(a*x1 +1)(a*x2 +1) =0 (1+a^2)x1x2 +a(x1+x2)+1 =0 ...(1) x1x2 =-2/(3-a^2), x1+x2 =2a/(3-a^2)代入(1), 得: a = 1,-1 2问见评论...

千问 · 2011-12-13 22:14:50

直径所对的圆心角等于90度...

千问 · 2011-12-13 22:14:50

正负1，连列方程，用ab表示，楼上的写的不对，二次项系数要讨论，这也是我今天的作业，真巧啊...

千问 · 2011-12-13 22:14:50

(3-a^2)x^2-2ax-1=0,x1+x2=2a/(3-a^2),x1x2=-2/(3-a^2),,OA⊥OB，x1x2+y1y2=0,-2(1+a^2)/(3-a^2)+a*2a/±1，y0=x0/2,x0=(x1+x2)/2,y0=(y1+y2)/2,2x0=2a/(3-a^2),ax1+1+ax2+1=x0,a1=2,a2=-3/2...

千问 · 2011-12-13 22:14:50

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