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《全日制十年制学校高中课本》第二册 (以下简称《课本》) 双曲线的方程是用右面一套准线和焦点推得的。教师在讲完这一内容时,学生往往会提问:“用其它的准线和焦点能否推出双曲线的方程?”为了对这个问题进行全面讨论,本文将用左、右两套准线和焦点分各种情况对双曲线两支曲线的方程进行推导,以求得对双曲线方程的进一步认识。取《课本》P179页例3:求圆锥曲线(到焦点和到准线的距离的比是е的点的轨迹) 的极坐标方程 (取е>1,即为双曲线方程)
The second volume of the “Full-time 10-year high school textbook” (hereinafter referred to as “textbook”) is a hyperbolic equation that is derived from the right set of guidelines and focus. When the teacher completes this content, students often ask questions: “Can you use other guidelines and focus to introduce hyperbolic equations?” In order to fully discuss this issue, this article will use the left and right sets of guidelines and Focusing on various conditions, the equations of the hyperbolic two-curve curves are deduced to obtain a further understanding of the hyperbolic equations. Take the textbook “page P179” Example 3: Find the polar equation of the conic curve (the ratio of the distance to the focus and the distance from the quasi-line to the е-point) (take е>1, that is, the hyperbolic equation)