Plotting an elliptical arc in TikZ with minimal additional packages and as simple as possible functions

Question

I have the above output from Mathematica that I would like to reproduce exactly in LaTeX, but I am just beginning with TikZ and do not understand the huge layers of code that are presented in other questions with similarly shaped elliptical arcs.

For that reason, I am not particularly interested in advanced packages, but if there is a package that allows me to do it using just the polar equation I will accept it as a solution.

I tried polar plotting but TikZ just breaks arbitrarily when I put in the polar form of the curve and for some reason ignores the square root.

Answer 1

\documentclass[tikz]{standalone}

\begin{document}
\begin{tikzpicture}
% 7/90*180=14
% -1/7*180=-25.71428571
% 6/7*180=154.2857143
  \draw
    [thick,color=black,domain=-25.71428571:154.2857143,samples=200,smooth]
 plot (xy polar cs:angle=\x,
        radius=
          {1/sqrt(1-0.9800139176438553*cos(\x-14)*cos(\x-14))});
\end{tikzpicture}
\end{document}

TikZ's cos and sin use degrees per default.