Trying to plot the equation of a circle of radius $5$ in LaTex

Question

I do not want to draw a circle. I want to use the plot function to plot the equation of a circle. I think there is a difference. Here is the equation of the circle I want to plot. $$ x^2 + y^2 = 25 $$.

Here is my attempt but it does not show a circule. It looks more like a parabola. What am I doing wrong?

\pgfplotsset{compat = newest}
Here is a circle.
\newline 
\begin{tikzpicture}
\begin{axis}[
xmin = -6, xmax = 6,
ymin = -5, ymax = 6,
]
\addplot[
domain = -5:5,
samples = 200,
smooth,
thick,
blue,
] { sqrt{ 25 - \x*\x } };
\end{axis}
\end{tikzpicture}

Answer 1

Though I am new to pgfplots but maybe this answer can point in the right direction --as copied from--

Plot circles on axis in pgfplots

Need to use axis equal=true to ensure that the scale used on the x-axis is the same as that on the y-axis. Otherwise, the circle will look like an ellipse.

I shifted the placement of the legend by setting legend style -- using --https://tex.stackexchange.com/a/227101/197451

\tikzset{My Style/.style={samples=100, thick}}%<----------------preamble
    \begin{tikzpicture}
    \begin{axis}[
    axis lines = middle,
    xlabel = $x$,
    ylabel = {$y$},
    axis equal=true,
    legend style={at={(0.5,-0.1)},anchor=north,
%       cells={anchor=west},
%       legend pos=north west,
%       legend image post style={yshift=1cm}
    },
    ]
%   \addplot [domain=-4:4, My Style, red] {2*x+1};
%   \addlegendentry{$y=2x+1$}
\addplot [domain=-3:3, My Style, blue] {sqrt(9-x^2)};
\addplot [domain=-3:3, My Style, blue] {-sqrt(9-x^2)};
\addlegendentry{$x^2+y^2=9$}

\end{axis}
\end{tikzpicture}

Answer 2

Firstly, in you example, sqrt{...} should be replaced with sqrt(...).

Next, My answer based on the example in pgfplots manual, sec. 4.23, shows that to draw a circle with polar coordinate system, you get smoother plot with fewer samples.

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat = newest}
\begin{document}
Here is a circle.
\newline 
\begin{tikzpicture}
  \begin{axis}[
    axis equal
  ]
    \addplot[
      domain = 0:2*pi,
      samples = 40,
      smooth,
      data cs=polar,
      thick,
      blue,
    ] (deg(x), 5);
  \end{axis}
\end{tikzpicture}
\end{document}