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www163707.com:高中数学第二章圆锥曲线与方程221双曲线的标准方程1导学案新人教B版选修11

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双曲线的标准方程(一) (自学自测) 【学习目标】理解双曲线的定义,掌握双曲线的标准方程的推导及标准方程 【重点】 :双曲线的定义及其标准方程。 【难点】 :双曲线标准方程的推导。 【自主学习】 : 阅读课本 49 页至 51 页,完成下列问题。 1、定义: 叫双曲线的焦点, 注意:若 若 叫做双曲线, 叫做焦距。 ,则动点的轨迹是射线(即 F1 F2 , F2 F1 的延长线) ; ,则动点的 轨迹不存在。 ; 2、焦点在 x 轴上的双曲线的标准方程为 焦点在 y 轴上的双曲线的标准方程为 。 其中 a,b,c 的关系是 【自我检测】 1、 。 ,焦点在 x 轴上,则双曲线的方程为 2、已知双曲线的方程为 3、如果双曲线 上一点 与焦点 ,则双曲线的焦点坐标为 的距离等于 8,则点 与焦点 的距离为 4、若焦点在 轴上,经过点 5、双曲线 的一个焦点坐标是 ;则双曲线的方程为 ,则 = 【自研自悟】 例 1、求适合下列条件的双曲线的标准方程。 (1)两 个焦点坐标分别是(-5,0),(5,0), 双曲线上的点与两焦点的距离之差的绝对值 等于 8 -1- (2)双曲线的一个焦点坐标 是(0,-6)经过点 A(-5,6) y2 x2 ? 1。(1) 求双曲线C的焦点F1 , F2的坐标 例 2、已知双曲线C的方程是 16 20 (2) 如果双曲线 C上一点P与焦点F1的距离等于 8,求点P与F2 的距离。 例 3、在相距 1400 米的 A, B 两个观察站,在 A 站听到炮弹爆炸声的时间比在 B 站听到时早 4 秒,已知当时声的速度是 340 米/秒,求炮弹爆炸点所在的曲线方程。 -2- 【收获总结】1、双曲线的定义 【自练自提】 1、已知双曲线的左 、右焦点分别为 么 的周长是 2、双曲线的标准方程及求法 ,在左支上过 的弦 的长为 5,若 ,那 2、根据下列条件,求双曲线的方程: (1)以椭圆 的短轴的两个端 点为 焦点,且过点 ; (2)以椭圆 的两个顶点为焦点,焦点为顶点。 -3-

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