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圆锥曲线中的定值问题是高考命题的一个热点,解答此类问题的基本策略有两种:一是把相关几何量特殊化,在特例中求出几何量的定值,再证明结论与特定状态无关;二是把相关几何量用曲线系里的参变量表示,再证明结论与求参数无关。一、证明某一代数式为定值例1(2013年山东卷,理22题)椭圆C:x~2/a~2+y~2/b~2=1(a>b>0)的左、右焦点分别是F_1、F_2,离心率为3~(1/2)/2,过F_1且垂直于x轴的直线被椭圆C截得的线段
The fixed value problem in the conic curve is a hot spot in the college entrance examination proposition. There are two basic strategies to solve this kind of problem: one is to specialize the relevant geometric quantity, find the fixed value of the geometric quantity in a special case, and then prove the conclusion and the specific The state has nothing to do; the second is related to the amount of geometry used in the curve of the parameters of the variable, and then prove that the conclusion has nothing to do with the parameters. First, to prove that a certain algebraic formula is given in Example 1 (2013 Shandong Volume, Theorem 22). The left side of the elliptic C: x ~ 2 / a ~ 2 + y ~ 2 / b ~ 2 = 1 (a> b> 0) , The right focal point is F_1, F_2, eccentricity is 3 ~ (1/2) / 2, F_1 and perpendicular to the x-axis of the line is the ellipse C section