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平面上的二次曲线共分为九类。对于一个任意给定的二元二次方程,根据其不变量,可以很容易地判断它表示何类曲线。若该方程的系数中含有参数,则它可以表示几种不同类型的曲线。在朱鼎勋、陈绍菱编《空间解析几何学》中,作为例子对具体给出的含参数的二元二次方程,详尽地讨论了当参数变动时它所表示的曲线的类型,并且配备了相应的习题。但在该书的例题及习题中,含一个参数的二元二次方程,所表示的曲线的不同类型,最多都没有超过七种。
The quadratic curves on the plane are divided into nine categories. For any given quadratic quadratic equation, based on its invariant, it can be easily judged what kind of curve it represents. If the coefficient of the equation contains parameters, it can represent several different types of curves. In Zhu Dingxun and Chen Shaoling’s “Spatial Analytic Geometry”, as an example of the binary quadratic equation with parameters specifically given, the type of the curve it represents when the parameter changes is discussed in detail, and is equipped with corresponding Exercises. However, in the examples and exercises of the book, the binary quadratic equation with one parameter shows no more than seven different types of curves.