全日制普通高级中学教科书数学(试验修订本)第二册(上)中有这样一道例题(§7.7例2). 已知圆的方程是x2+y2=r2,求经过圆上一点M(x0,y0)的切线的方程. 解(略)所求切线方程为xx0+yy0=r2. 此切线方程简捷明了,体现了数学美,这里我们也许会想到当M(x0,y0)在圆x2+y2=r2的内部、外部时方程xx0+yy0=r2有何几何意义呢? 定理1 已知圆的方程是x2+y2=r2,点 There is such an example (§7.7 Example 2) in full-time ordinary high school textbook mathematics (test revision) Book 2 (top). The equation of the circle is known as x2+y2=r2. Find the circle passing through a point M (x0). Tangent equation of y0). Solution (slightly) The tangent equation is xx0+yy0=r2. This tangent equation is simple and clear, which embodies the beauty of mathematics. Here we may think of when M(x0, y0) is in the circle x2+. What is the geometric meaning of the equation xx0+yy0=r2 when y2=r2 is inside or outside? Theorem 1 The equation of the known circle is x2+y2=r2,