求一道数学题 已知椭圆x²/16+y²/4=1,过点(2.1)做一弦 使弦在这点被平分,求直线方程
人气:301 ℃ 时间:2020-03-28 17:26:16
解答
点差法
设两交点(x1,y1)(x2,y2)
满足方程x1²/16+y1²/4=1 x2²/16+y2²/4=1
两式相减(x1²-x2^2)/16+(y1²-y2^2)/4=0
(y1-y2)/(x1-x2)=-(x1+x2)/4(y1+y2)=-1/2
即直线斜率为-1/2
方程为y-1=-1/2(x-2) =>x+2y-4=0
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