设$k_1,k_2$分别为$AC,BD$斜率,四边形面积表达式为
\[S=2{{a}^{2}}{{b}^{2}}|k_1-k_2|\frac{\sqrt{{{a}^{2}}k_{1}^{2}+{{b}^{2}}-m_{1}^{2}}\sqrt{{{a}^{2}}k_{2}^{2}+{{b}^{2}}-m_{2}^{2}}}{({{a}^{2}}k_{1}^{2}+{{b}^{2}})({{a}^{2}}k_{2}^{2}+{{b}^{2}})},\]
其中\[{{m}_{1}}={{y}_{0}}-{{k}_{1}}{{x}_{0}},\;\;\;{{m}_{2}}={{y}_{0}}-{{k}_{2}}{{x}_{0}}.\] |