硬解

根据

x2M+y2N=1,Ax+By+C=0\dfrac{x^2}{M}+\dfrac{y^2}{N}=1, Ax+By+C=0

可解出

(MA2+NB2)x2+2MACx+M(C2−NB2)=0(MA2+NB2)y2+2NBCy+N(C2−MA2)=0x1y2+x2y1=2MANBMA2+NB2Δx=4MNB2(MA2+NB2−C2)Δy=4MNA2(MA2+NB2−C2)\begin{align} &(MA^2+NB^2)x^2+2MACx+M(C^2-NB^2)=0 \\ &(MA^2+NB^2)y^2+2NBCy+N(C^2-MA^2)=0 \\ &x_{1}y_{2}+x_{2}y_{1}=\frac{2MANB}{MA^2+NB^2} \\ &\Delta_{x}=4MNB^2(MA^2+NB^2-C^2) \\ &\Delta_{y}=4MNA^2(MA^2+NB^2-C^2) \\ \end{align}