我使用 Geogebra 通过平面上的五个已知点绘制一条双曲线。然后我使用 intern 命令将我的图形转换为 tikz 代码。我创建了一个文件源代码 latex/tikz，但编译后（pdfLaTeX），点被绘制出来了，但不是五个点的正确双曲线。
问题：有人知道如何在 TikZ 源中直接用五个点绘制最简单的圆锥曲线吗？如果我只知道 f(x,y)=0 方程，我可以画双曲线吗？
感谢这项研究！D. Collin
% % % % 通过导出 pgf/TikZ 生成的代码是：
% ---------
\documentclass[10pt]{article}
\usepackage{pgf,tikz}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}
\definecolor{xdxdff}{rgb}{0.4902,0.4902,1}
\definecolor{zzqqzz}{rgb}{0.6,0,0.6}
\definecolor{qqzzqq}{rgb}{0,0.6,0}
\definecolor{uququq}{rgb}{0.25098,0.25098,0.25098}
\definecolor{ffqqtt}{rgb}{1,0,0.2}
\definecolor{qqqqff}{rgb}{0,0,1}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\clip(-6,-6) rectangle (6,6);
\draw[line width=0.4pt] (-3.24171,-0.87914) -- (-3.16257,-0.72086) -- (-3.32086,-0.64171) -- (-3.4,-0.8) -- cycle;
\draw[line width=0.4pt] (-2.70156,-2.99384) -- (-2.67081,-2.81957) -- (-2.84508,-2.78881) -- (-2.87584,-2.96309) -- cycle;
\draw[line width=0.4pt] (0.37519,-4.37497) -- (0.35016,-4.19978) -- (0.17497,-4.22481) -- (0.2,-4.4) -- cycle;
\draw[line width=0.4pt] (2.71507,-4.46302) -- (2.56435,-4.37027) -- (2.4716,-4.52098) -- (2.62232,-4.61373) -- cycle;
\draw [samples=50,domain=-0.99:0.99,rotate around={-157.68231:(-4.98202,-2.15901)},xshift=-4.98202cm,yshift=-2.15901cm,line width=2pt,color=ffqqtt] plot ({2.47764*(1+\x^2)/(1-\x^2)},{1.88916*2*\x/(1-\x^2)});
\draw [samples=50,domain=-0.99:0.99,rotate around={-157.68231:(-4.98202,-2.15901)},xshift=-4.98202cm,yshift=-2.15901cm,line width=2pt,color=ffqqtt] plot ({2.47764*(-1-\x^2)/(1-\x^2)},{1.88916*(-2)*\x/(1-\x^2)});
\draw [line width=1.2pt,color=qqqqff] (-1,4)-- (-2,2);
\draw [line width=1.2pt,color=qqqqff] (-2,2)-- (-2.6,-1.4);
\draw [line width=1.2pt,color=qqqqff] (-2.6,-1.4)-- (0,-3);
\draw [line width=1.2pt,color=qqqqff] (0,-3)-- (-1,4);
\draw [line width=1.2pt,dash pattern=on 2pt off 2pt,color=qqzzqq] (3,-4)-- (-3.4,-0.8);
\draw [line width=1.2pt,dash pattern=on 2pt off 2pt,color=qqzzqq] (3,-4)-- (2.62232,-4.61373);
\draw [line width=1.2pt,dash pattern=on 2pt off 2pt,color=zzqqzz] (3,-4)-- (0.2,-4.4);
\draw [line width=1.2pt,dash pattern=on 2pt off 2pt,color=zzqqzz] (3,-4)-- (-2.87584,-2.96309);
\draw [dash pattern=on 2pt off 2pt,color=qqqqff] (-2,2)-- (-3.71193,-1.42386);
\draw [dash pattern=on 2pt off 2pt,color=qqqqff] (-2.6,-1.4)-- (-3.11831,-4.33711);
\draw [dash pattern=on 2pt off 2pt,color=qqqqff] (0,-3)-- (0.27455,-4.92186);
\draw [dash pattern=on 2pt off 2pt,color=qqqqff] (0,-3)-- (3.39975,-5.09215);
\fill [color=qqqqff] (-1,4) circle (1.5pt);
\draw[color=qqqqff] (-1.14371,4.25851) node {$M_1$};
\fill [color=qqqqff] (-2,2) circle (1.5pt);
\draw[color=qqqqff] (-2.07806,2.2897) node {$M_2$};
\fill [color=qqqqff] (-2.6,-1.4) circle (1.5pt);
\draw[color=qqqqff] (-2.77882,-1.36427) node {$M_3$};
\fill [color=qqqqff] (0,-3) circle (1.5pt);
\draw[color=qqqqff] (0.30787,-2.78248) node {$M_4$};
\fill [color=qqqqff] (3,-4) circle (1.5pt);
\draw[color=qqqqff] (3.27776,-3.70015) node {$M_5$};
\fill [color=uququq] (0.2,-4.4) circle (1.5pt);
\draw[color=uququq] (-0.02583,-4.35086) node {$H_{14}$};
\fill [color=uququq] (-2.87584,-2.96309) circle (1.5pt);
\draw[color=uququq] (-3.0291,-2.83254) node {$H_{23}$};
\fill [color=uququq] (2.62232,-4.61373) circle (1.5pt);
\draw[color=uququq] (2.56032,-4.70124) node {$H_{34}$};
\fill [color=uququq] (-3.4,-0.8) circle (1.5pt);
\draw[color=uququq] (-3.49627,-0.46329) node {$H_{12}$};
\fill [color=xdxdff] (4.0018,-4.30299) circle (1.5pt);
\draw[color=xdxdff] (4.11201,-4.0839) node {$E$};
\fill [color=xdxdff] (-0.46313,5.00435) circle (1.5pt);
\draw[color=xdxdff] (-0.64317,5.19286) node {$F$};
\end{tikzpicture}
\end{document}
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