metade de uma hipérbole

Question

Apenas a parte superior da metade da minha hipérbole está entrando corretamente. A outra metade está fazendo algo estranho:

\documentclass{article}
\usepackage{tikz, pgf}
\begin{document}
\begin{center}
  \begin{tikzpicture}
    \begin{scope}
      \clip (0,-3) rectangle (4,3);
      \draw [samples = 50, domain = -0.99:0.99,
      rotate around = {0:(0,0)}, xshift = 0cm, yshift = 0cm]
      plot ({0.69*(1+\x^2)/(1-\x^2)}, {0.72*2*\x/(1-\x^2)});
    \end{scope}
  \end{tikzpicture}
\end{center}
\end{document}

Answer 1

Substituir \x*\xou (\x)^2por \x^2corrige seu problema.

\documentclass{article}
\usepackage{tikz, pgf}
\begin{document}
\begin{center}
  \begin{tikzpicture}
    \begin{scope}
      \clip (0,-3) rectangle (4,3);
      \draw [samples = 50, domain = -0.99:0.99,
      rotate around = {0:(0,0)}, xshift = 0cm, yshift = 0cm]
      plot ({0.69*(1+\x*\x)/(1-\x*\x)}, {0.72*2*\x/(1-\x*\x)});
    \end{scope}
  \end{tikzpicture}
\end{center}
\end{document}

Answer 2

Com PSTricks.

\documentclass[pstricks,border=12pt]{standalone}
\usepackage{pst-plot,pst-math}
\def\X(#1){COSH(#1)}
\def\Y(#1){SINH(#1)}
\psset{algebraic}
\begin{document}
\begin{pspicture}(-6,-4)(6,4)
    \psaxes{->}(0,0)(-6,-4)(5.5,3.5)[$x$,0][$y$,90]
    \psset{linecolor=blue}
    \psparametricplot{-2}{2}{\X(t)|\Y(t)}
    \psparametricplot{-2}{2}{-\X(t)|\Y(t)}
\end{pspicture}
\end{document}