浅谈双曲线的定义及应用

• 作 者: 赵建勋
• 机 构: 正定中学 河北050800
• 出 处: 数学通讯
• 发表日期: 2004年24期
• 关键词: 轨迹方程 定义法 离心率 简化运算 正弦定理 平分线 题设 直角坐标系 韦达 轴长

课本指出 :平面内与两个定点F1,F2 的距离的差的绝对值等于常数 (小于 |F1F2 |)的点的轨迹叫双曲线 ,这两个定点叫双曲线的焦点 .对此定义的理解时应注意以下三点 :1)注意点到两定点的距离差的绝对值是常数 ,且常数小于 |F1F2 |.没有绝对值 ,其轨迹只能是双曲线的一支 .2 )注意

The textbook points out that the trajectory of the point where the absolute value of the difference between the distances in the plane and the two fixed points F1, F2 is equal to a constant (less than |F1F2|) is called a hyperbola. These two fixed points are called hyperbolic focal points. Understanding of this definition The following three points should be noted: 1) Note that the absolute value of the distance difference between the two fixed points is constant, and the constant is less than |F1F2 |. There is no absolute value, and its trajectory can only be a hyperbolic one.