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Last edited by 青青子衿 2019-6-16 10:21\[\Delta_1=\frac{p^2}{a^2}+\frac{q^2}{b^2}+\frac{r^2}{c^2}-\frac{\left(qu-pv\right)^2}{a^2b^2}-\frac{\left(rv-qw\right)^2}{b^2c^2}-\frac{\left(ru-pw\right)^2}{a^2c^2}\]
\[l=\dfrac{2\sqrt{\Delta_1}}{\dfrac{p^2}{a^2}+\dfrac{q^2}{b^2}+\dfrac{r^2}{c^2}}\]
\[\varGamma\colon\,\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}=1\]
\begin{cases}
x=u+p\,t\\
y=v+q\,t\\
x=w+r\,t
\end{cases}
\begin{gather*}
x_{\overset{\,}1}=\frac{\frac{q^2u}{b^2}+\frac{r^2u}{c^2}-\frac{pqv}{b^2}-\frac{prw}{c^2}+p\sqrt{\frac{p^2}{a^2}+\frac{q^2}{b^2}+\frac{r^2}{c^2}-\frac{\left(qu-pv\right)^2}{a^2b^2}-\frac{\left(rv-qw\right)^2}{b^2c^2}-\frac{\left(ru-pw\right)^2}{a^2c^2}}}{\frac{p^2}{a^2}+\frac{q^2}{b^2}+\frac{r^2}{c^2}}\\
y_{\overset{\,}1}=\frac{\frac{p^2v}{a^2}+\frac{r^2v}{c^2}-\frac{pqu}{a^2}-\frac{qrw}{c^2}+q\sqrt{\frac{p^2}{a^2}+\frac{q^2}{b^2}+\frac{r^2}{c^2}-\frac{\left(qu-pv\right)^2}{a^2b^2}-\frac{\left(rv-qw\right)^2}{b^2c^2}-\frac{\left(ru-pw\right)^2}{a^2c^2}}}{\frac{p^2}{a^2}+\frac{q^2}{b^2}+\frac{r^2}{c^2}}\\
z_{\overset{\,}1}=\frac{\frac{p^2w}{a^2}+\frac{q^2w}{b^2}-\frac{pru}{a^2}-\frac{qrv}{b^2}+r\sqrt{\frac{p^2}{a^2}+\frac{q^2}{b^2}+\frac{r^2}{c^2}-\frac{\left(qu-pv\right)^2}{a^2b^2}-\frac{\left(rv-qw\right)^2}{b^2c^2}-\frac{\left(ru-pw\right)^2}{a^2c^2}}}{\frac{p^2}{a^2}+\frac{q^2}{b^2}+\frac{r^2}{c^2}}
\end{gather*}
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