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2001年全国高考试题(广东、河南卷)第21题:已知椭圆 x~2/2+y~2=1的右准线 l 与 x 轴交于一点 E,过椭圆右焦点 F 的直线与椭圆相交于 A、B 两点,点 C 在右准线 l 上,且 BC∥x轴,求证直线 AC 经过线段 EF 的中点.笔者经研究发现,一般的椭圆都能得到此结论,而且对一般的双曲线、抛物线也可以到出此结论,由此得到圆锥曲线的一个一般性结论:已知圆锥曲线的一条准线 l 与 x 轴交于一点 E,过与此准线相应的焦点 F 的直线与圆锥曲线相交于 A、B 两点,点 C 在此准线 l 上,且
2001 National Examination Questions (Guangdong, Henan) Question 21: The right guideline l of the known ellipse x~2/2+y~2=1 crosses the x axis at point E, and the straight line passing through the right ellipse F of the ellipse. The ellipse intersects at two points A and B, and point C is at the right guideline l, and the BC∥x axis confirms the straight line AC passing through the middle point of the line segment EF. The authors found that the general ellipse can reach this conclusion, and The general hyperbola and parabola can also come to this conclusion, from which a general conclusion of the conic curve is obtained: a guideline l of the conic curve is known to intersect with the x-axis at a point E, and the focus corresponding to this guideline is given. The straight line intersects with the conic curve at two points A and B, and the point C lies above this line l, and