How to find the x value and the y value in a point in a pgfplot

Question

I want to know the x value and the y value on a pgfplot area to draw a line. How to find it?

For an example, I need to draw a line from the X label to the Y label; to do so I need to get the x value and the y value of the labels to fill the \pslineoptions thing.

I am using Texmaker + Miktex.

screenshot of the texmaker window

MWE

\documentclass[12pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{pgfplots}\pgfplotsset{compat=1.18}

\author{Some dude's name}
\begin{document}
\begin{tikzpicture}
\begin{axis}
[
    xlabel={x}, 
    ylabel={y}, 
    grid, 
    ticks=none
]
\addplot3[blue, no marks, surf, domain=0:1, samples=50] {25-5*x*x -y*y};

\end{axis}
\end{tikzpicture}
\end{document}

Answer 1

You can use normal TikZ commands in pgfplots; the only problem is to identify which coordinate system you want and avoid clipping if you need it.

In the case of 3d graphs, the relevant part is around page 359 of the manual. You have to take care of precedence yourself to avoid the line above the graph, if needed...

\documentclass[12pt,a4paper]{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{tikz}
\usepackage{pgfplots}\pgfplotsset{compat=1.18}

\author{Some dude's name}
\begin{document}
\begin{tikzpicture}
\begin{axis}
[
    xlabel={x},
    ylabel={y},
    grid,
    ticks=none,
    % clip mode=individual,
]

\draw [thick, blue] (rel axis cs:0.5,0,0) -- (rel axis cs:0.5,1,0);
\addplot3[blue, no marks, surf, domain=0:1, samples=10] {25-5*x*x -y*y};
\draw [thick, red] (rel axis cs:0.5,0,0) -- (rel axis cs:1,0.5,0);

\end{axis}
\end{tikzpicture}
\end{document}

PD notice that \usepackage[utf8]{inputenc} is default since 2018 and not needed, but you probably want \usepackage[T1]{fontenc}...