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已知圆锥曲线上存在不同的两点关于直线成轴对称,求直线或圆锥曲线中参数的取值范围,是轴对称中求解综合性强且处理方法灵活多样的一类问题.由于双曲线分平面所成的区域最复杂,我们先看一个以双曲线为背景的问题.题1已知双曲线C:x216-y29=1,直线l:y=x+m.(1)试确定m的取值范围,使得双曲线的左支和右支上各有一点关于直线l对称;(2))试确定m的取值范围,使得双曲线的同支上有不同的两点关于直线l对称.下面先给出这个问题的两种解法.
It is known that there are two different points on the conic and the axis is symmetrical about the straight line, and the range of the parameter in the straight line or conic is a kind of problem that the comprehensiveness is strong and the processing method is flexible in axisymmetry. The area that the plane makes is the most complicated, let’s look at a problem that takes the hyperbola as the background. Problem 1 is known Hyperbolic C: x216-y29 = 1, straight line l: y = x + m. The range of values, so that the hyperbolic left and right branches have a little on the line l symmetry; (2)) try to determine the value of m range, so that hyperbolic on the same branch have two different points on the line l symmetry Here are two solutions to this problem.