本文拟以三类最值问题为例,谈谈怎样运用解析几何知识,巧求它们的最值。先复习几组直线与二次曲线相切的关系式:1.直线y=kx+m(m≠0)与圆(x-x_o)~2+(y-y_o)~2=r~2相切的充要条件是k~2r~2+r~2=(kx_o-y_o+m)~2——公式1.1. 推论:直线y=kx+m与圆x~2+y~2=r~2相切的充要条件是k~2r~2+r~2=m~2—— This paper proposes to use the three kinds of most-valued problems as an example to talk about how to use analytical geometry knowledge and how to get the best of them. First review the relationship between several sets of lines tangent to the quadratic curve: 1. Line y=kx+m(m≠0) and circle (x-x_o)~2+(y-y_o)~2=r~2 The necessary and sufficient condition for cutting is k~2r~2+r~2=(kx_o-y_o+m)~2 - Equation 1.1. Corollary: The straight line y=kx+m and the circle x~2+y~2=r~ The necessary and sufficient conditions for tangent 2 are k~2r~2+r~2=m~2~