笔者在教学圆一节时,有学生提出了两个很有意思的问题:1.已知圆的方程x2+y2=r2,求经过圆上一点M(x0,y0)的切线方程。这是课本中一道可作结论用的例题,答案是x0x+y0y=r2。他们提出如果点M不在圆上,直线x0x+y0y=r2。又是客观存在的,那么它与圆有怎样的关系呢? In the teaching circle of the author, some students raised two very interesting questions: 1. Known circle equation x2 + y2 = r2, find the tangent equation passing a point M (x0, y0) on the circle. This is an example of a conclusion that can be used in a textbook. The answer is x0x+y0y=r2. They propose that if point M is not on the circle, the line x0x+y0y=r2. It is also an objective reality. How does it relate to circles?