回復 5# leo790124 的帖子
第4題
令\(A({{x}_{1}},{{y}_{1}}),B({{x}_{2}},{{y}_{2}}),C({{x}_{3}},{{y}_{3}})\)
\(\begin{align}
& \left\{ \begin{align}
& {{y}^{2}}=4cx \\
& 4x+y-20=0 \\
\end{align} \right. \\
& {{y}^{2}}+cy-20c=0 \\
& {{y}_{2}}+{{y}_{3}}=-c \\
& {{x}_{2}}+{{x}_{3}}=\frac{20-{{y}_{2}}}{4}+\frac{20-{{y}_{3}}}{4}=10+\frac{c}{4} \\
& \frac{{{y}_{1}}+{{y}_{2}}+{{y}_{3}}}{3}=0,{{y}_{1}}=c \\
& {{x}_{1}}=\frac{{{y}_{1}}^{2}}{4c}=\frac{c}{4} \\
& \frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}{3}=c \\
& \frac{\frac{c}{4}+10+\frac{c}{4}}{3}=c \\
& c=4 \\
\end{align}\)
