最近学解析几何，发现很多题可以直接套通解，于是把通解求了个遍。
点和点
-
求 \(P_1(x_1,y_1)\)、\(P_2(x_2,y_2)\) 所在的直线
\(\left(y_{2}-y_{1}\right)x+\left(x_{1}-x_{2}\right)y+x_{2}y_{1}-x_{1}y_{2}=0\)
-
求 \(P_1(x_1,y_1)\)、\(P_2(x_2,y_2)\) 连线的中垂线 \(l\)
\(l:\left \{\begin{array}{l} \left(x_{1}-x_{2}\right)\left(2x-x_{1}-x_{2}\right)+\left(y_{1}-y_{2}\right)\left(2y-y_{1}-y_{2}\right)=0 \\ 2\left(x_{1}-x_{2}\right)x+2\left(y_{1}-y_{2}\right)y+x_{2}^{2}-x_{1}^{2}+y_{2}^{2}-y_{1}^{2}=0 \end{array}\right.\)
直线和点
-
求 \(P_0(x_0,y_0)\) 关于直线 \(l: Ax+By+C=0\) 对称所得点 \(P_0'\)
\(T=\frac{Ax_{0}+By_{0}+C}{A^{2}+B^{2}}\\P_0'\left(x_{0}-2AT,y_{0}-2BT\right)\)