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“三线共点”问题是双曲线中较为常见的问题.通常可以先联立两条直线方程,求出交点,再将交点坐标代入第三条直线方程中来验证.这类问题的解决往往要结合双曲线的定义、几何性质,变化较多,难度较大.下面以一道联考题引入并作一些探究.例1已知双曲线(x~2)/(a~2)-(y~2)/(b~2)=1(a>0,b>0)的左,右焦点分别为F_1,F_2,过点F1作圆x~2+y~2=a~2的一条切线分别交双曲线的左,右
The problem of “three lines of common point ” is the more common problem in hyperbola.Usually, we can establish the intersection of two linear equations and find the intersection point, and then put the intersection point into the third equation of line to verify. Often associated with the definition of hyperbolic, geometric properties, changes more difficult and more difficult to introduce the following as a joint test and make some exploration.Example 1 known hyperbola (x ~ 2) / (a ~ 2) - (y The left and right focal points of ~ 2) / (b ~ 2) = 1 (a> 0, b> 0) are F_1 and F_2, respectively. Respectively, cross the hyperbola left and right