圆锥曲线从出现到现在已经有数千年的历史,帮助人类认识自然、探索宇宙空间的奥秘,在今天的高中数学的教学中也占有十分重要的地位。苏教版高中数学教材采用了古希腊数学家阿波罗尼的思想:使用一个平面截取圆锥面的办法,通过改变平面相对圆锥面的位置,可以分别得到椭圆、双曲线、抛物线。让学生感官上感受“圆锥曲线”这统一概念,从而也有了圆锥曲线的第一定义:平面内到两定点的距离和为常数(大于)的点的轨迹为椭圆;平面内到两定点的距离差为常数(小于)的点的轨迹为双曲线;平面内到定点的距离等于其到定直线(定点不在定直线上)的距离的点的轨迹为抛物线。在圆锥曲线章节的最后一节,教材又给出了圆锥曲线的统一定义(第二定义):平面内到定点的距离与其到定直线(定点不在定直线上)的距离的比等于常数的点的轨迹。不少学生有了“柳暗花明又一村”的感觉,极大激发了学生求知欲。有的学生不禁要问,圆锥曲线还有其它的 The conic curve has existed for thousands of years from its appearance till now. It helps mankind understand nature and explore the mysteries of space. It plays a very important role in today’s high school mathematics teaching. Suyao version of high school mathematics textbooks used the ancient Greek mathematician Apollonian thought: the use of a plane truncated cone approach, by changing the plane relative to the position of the conical surface, you can get oval, hyperbolic, parabolic. Let the students feel the unified conception of “conic curve ” so that there is also the first definition of conic curve: the distance between two fixed points in the plane and the point of constant (larger than) are oval; Is a hyperbolic curve, and the trajectory of a point within a plane to a fixed point at a distance equal to the distance from the fixed line (the fixed point is not on the fixed line) is a parabola. In the last section of the conic section, the text gives a uniform definition of the conic (second definition): the distance from the in-plane to the fixed point to the point at which the distance to the fixed line (not on the fixed point) is equal to the constant traces of. Many students have the feeling of “vista”, greatly stimulated students curiosity. Some students can not help but ask, there are other conic curves