求抛物线y^2=x的一组斜率为2的平行弦的中点的轨迹方程.(用点差法)
人气:455 ℃ 时间:2019-08-21 11:48:05
解答
点差法,设此平行弦与y^2=x交于(X1,Y1),(X2,Y2)
y1^2=x1 y2^2=x2
两个式子相减,y1^2-y2^2=x1-x2
(y1+y2)(y1-y2)=x1-x2
(y1-y2)/(x1-x2)=1/(y1+y2)
发现y1-y2/x1-x2,就是斜率2,且y1+y2=2y
故轨迹是Y=1/4,取型内部分
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