对于直线l:y=kx+1是否存在这样的实数,使得L与双曲线C:3x^2+y^2=1的交点A,B关于直线y=ax（a为常数）对称？

显示全部楼层 · 2013-4-3 14:39:56

let A(x1,y1), B(x2,y2)y=kx+1
(1)3x^2+y^2 =1
(2)sub (1) into (2)3x^2+ (kx+1)^2 =1(3+k^2)x^2+ 2kx =0(x1+x2)/2 =-k/(3+k^2) = xSimilarly3[(y-1)/k]^2 +y^2 = 1(3+k^2)y^2-6y +3-k^2 =0(y1+y2)/2 = 3/(3+k^2)=ymid point of A,B = ( x,y) =( -k/(3+k^2), 3/(3+k^2) )for y=ax3/(3+k^2) = -a...

千问 · 2013-4-3 14:39:56

C:3x^2-y^2=1，L:y=kx+1，交点A(0,1),(2k/(3-k^2),B(k^2+3)/ (3-k^2))A,B关于S：y=ax对称，则AB中点在S上，xs=k/(3-k^2),ys=3/ (3-k^2),代入S方程，3/ (3-k^2)=a* k/(3-k^2),3=a*k,k=3/a...