论文部分内容阅读
在解析几何中,椭圆、双曲线、抛物线往往有相同或类似的一些性质.本文通过椭圆中一个斜率乘积为定值问题引入,通过探究,进行拓展与推广,得到一般性的结论,从中可以感受到数学问题的“形异质同”.引入如图1,已知椭圆C:x24+y23=1的左、右焦点分别为F1,F2,过右焦点F2斜率为k(k≠0)的直线l与椭圆C相交于E,F两点,A为椭圆的右顶点,直线AE,AF分别交直线x=3于点M,N,线段MN的中点为P,记直线PF2的斜率为k′.
In analytic geometry, elliptic, hyperbola and parabola tend to have the same or similar properties.In this paper, we introduce a slope product of the ellipse as a fixed value problem, explore and expand and popularize it to get a general conclusion, from which we can feel To the mathematical problem “heterogeneous with the same shape.” Introduced in Figure 1, known oval C: x24 + y23 = 1 left and right focus respectively F1, F2, right focus F2 slope k (k ≠ 0 ) Of the line l intersects with the ellipse C in the E, F two points, A is the right apex of the ellipse, the line AE, AF were cross-line x = 3 at the point M, N, The slope is k ’.