斜率为2的直线L与双曲线2(x2)—3(y2)=6交于A、B两点,AB=4,求直线L的方程.

斜率为2的直线L与双曲线2(x2)—3(y2)=6交于A、B两点,AB=4,求直线L的方程.
斜率为2的直线L与双曲线2(x2)—3(y2)=6交于A、B两点,AB=4,求直线L的方程.

斜率为2的直线L与双曲线2(x2)—3(y2)=6交于A、B两点,AB=4,求直线L的方程.
设.直线方程为y=2x+m 与双曲线2(x2)—3(y2)=6交于 所以 2x^2-3(2x+m)^2=6 2x^2-12x^2-12mx-3m^2-6=0 10x^2+12mx+(3m^2+6)=0 x1+x2=-12m/10=-6m/5 x1x2=(3m^2+6)/10 所以(x1-x2)^2=(x1+x2)^2-4x1x2=36m^2/25-2(3m^2+6)/5=(6m^2-60)/25 (y1-y2)^2=[(2x1+m)-(2x2+m)]^2=4(x1-x2)^2=4*(6m^2-60)/25 所以与双曲线2(x2)—3(y2)=6交于A、B两点AB^2=(x1-x2)^2+(y1-y2)^2=5*(6m^2-60)/25=4^2 (6m^2-60)/5=16 m^2=70/3 m=±√210/3 所以y=2x+√210/3和y=2x-√210/3

y=2x+m 代入双曲线 2x^2-3(2x+m)^2=6 2x^2-12x^2-12mx-3m^2-6=0 10x^2+12mx+(3m^2+6)=0 x1+x2=-12m/10=-6m/5 x1x2=(3m^2+6)/10 (x1-x2)^2=(x1+x2)^2-4x1x2=36m^2/25-2(3m^2+6)/5=(6m^2-60)/25 (y1-y2)^2=[(2x1+m)-(2x2+m)...

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y=2x+m 代入双曲线 2x^2-3(2x+m)^2=6 2x^2-12x^2-12mx-3m^2-6=0 10x^2+12mx+(3m^2+6)=0 x1+x2=-12m/10=-6m/5 x1x2=(3m^2+6)/10 (x1-x2)^2=(x1+x2)^2-4x1x2=36m^2/25-2(3m^2+6)/5=(6m^2-60)/25 (y1-y2)^2=[(2x1+m)-(2x2+m)]^2=4(x1-x2)^2=4*(6m^2-60)/25 所以AB^2=(x1-x2)^2+(y1-y2)^2=5*(6m^2-60)/25=4^2 所以(6m^2-60)/5=16 m^2=70/3 m=±√210/3 所以y=2x+√210/3和y=2x-√210/3

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