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2015年全国卷Ⅰ文科数学第20题以椭圆为载体,重点考查直线和椭圆的位置关系,题目的设置较简单.笔者对题目进行了多解分析,并经过推广探究得到三个一般性的结论.一、原题呈现已知椭圆C:(x~2)/(a~2)+(y~2)/(b~2)=1(a>b>0)的离心率为(2~(1/2))/2,点(2,2~(1/2))在C上.
2015 Volume I liberal arts mathematics 20 questions with oval as the carrier, the focus of examination of the relationship between the position of the line and the ellipse, the subject is relatively simple to set up. The author conducted a multi-solution analysis of the subject, and through the promotion of inquiry to get three general conclusions First, the original title shows that the eccentricity of the elliptical C (x ~ 2) / (a ~ 2) + (y ~ 2) / (b ~ 2) = 1 (a> b> 0) (1/2)) / 2, point (2,2 ~ (1/2)) is on C.