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现行中学数学教材中,选编了大量的二次曲线的切线问题。解决此类问题一般是用二次方程的判别式法。因为直线和圆相切的充要条件是它们有唯一的公共点,这一几何事实反映在代数方程上就是有重根,所以用判别式法解决圆的切线问题理由是充足的。但仅有一个公共点的切线定义对抛物线和双曲线不再适用了,那么用判别式法讨论这两类曲线的切线问
In the current middle school mathematics textbooks, a large number of tangent problems of the quadratic curve have been selected and compiled. Solving such problems is generally a discriminative method using a quadratic equation. Because the necessary and sufficient condition for the tangency of the straight line and the circle is that they have the only common point, this geometric fact is reflected in the algebraic equations. There are multiple roots, so the reason for using the discriminant method to solve the round tangent problem is sufficient. However, the tangent definition of only one common point is no longer applicable to parabola and hyperbola. Then the discriminant method is used to discuss the tangent of these two types of curves.