[Tex/LaTex] “Nice” 2D ellipse in 3D space

Question

I would like to draw a "nice" 2D ellipse in 3D space using tikz. I'm using the tikz packages and tikz library arrows.meta

\usepackage{tikz}
\usetikzlibrary{arrows.meta}

This is my code so far:

\begin{tikzpicture}[scale=2.0, line cap=round, line join=round, >=Triangle]
\draw [->] (0,-1.75) -- (0,1.75); %z
\draw [->] (0.81,1.05) -- (-0.81,-1.05); %x
\draw [->] (-2.35,0) -- (2.35,0); %y
\draw (-1.15,-1.01) node[anchor=north west] {\Large $ {x}$};
\draw (2.40,0.15) node[anchor=north west] {\Large $ {y}$};
\draw (-0.05,2.20) node[anchor=north west] {\Large $ {z}$};
\draw[color=red, rotate around={25:(0,0)}] (0,0) ellipse (2.5cm and 1.00cm);
\draw [fill] (0,0) circle (1.5pt);
\end{tikzpicture}

This code produces the plot below

Is there any way to improve the 3D effect of the ellipse in 3D space?

Answer 1

Here are two possibilities, depending on whether the elliptical plane is presumed to be in the x-y plane or not.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta}
\begin{document}
\begin{tikzpicture}[scale=2.0, line cap=round, line join=round, >=Triangle]
\draw [->] (0,-1.75) -- (0,1.75); %z
\draw [->] (0.81,1.05) -- (-0.81,-1.05); %x
\draw [->] (-2.35,0) -- (2.35,0); %y
\draw (-1.15,-1.01) node[anchor=north west] {\Large $ {x}$};
\draw (2.40,0.15) node[anchor=north west] {\Large $ {y}$};
\draw (-0.05,2.20) node[anchor=north west] {\Large $ {z}$};
\draw[color=red, rotate around={25:(0,0)}] (0,0) ellipse (2.5cm and 1.00cm);
\draw [fill] (0,0) circle (1.5pt);
\draw [->, red] (0,0) -- (0,0.5); %z
\draw (0.05,0.70) node[anchor=north west] {\Large $ {\hat n}$};
\end{tikzpicture}

\begin{tikzpicture}[scale=2.0, line cap=round, line join=round, >=Triangle]
\draw [->] (0,-1.75) -- (0,1.75); %z
\draw [->] (0.81,1.05) -- (-0.81,-1.05); %x
\draw [->] (-2.35,0) -- (2.35,0); %y
\draw (-1.15,-1.01) node[anchor=north west] {\Large $ {x}$};
\draw (2.40,0.15) node[anchor=north west] {\Large $ {y}$};
\draw (-0.05,2.20) node[anchor=north west] {\Large $ {z}$};
\draw[color=red, rotate around={25:(0,0)}] (0,0) ellipse (2.5cm and 1.00cm);
\draw [fill] (0,0) circle (1.5pt);
\draw [->, red] (0,0) -- (-.2,0.5); %z
\draw (-0.47,0.70) node[anchor=north west] {\Large $ {\hat n}$};
\end{tikzpicture}
\end{document}