Plot Tikz graph defined with two variables, ie 4=x^2+y^2

Question

I want to plot a graph of 4=(x-2)^2+(y-2)^2, How do I do that within tikz plot? I have tried re-arranging but it just throws errors at me! \draw [domain=0:4] plot ({\x},{2-\sqrt{4\x-\x*\x}}); Is there an easy way for me to type a graph like this easily, I would appreciate it if the re-arrange was unnecissary!

Answer 1

What is causing the error is your use of \sqrt instead of sqrt. The former is a macro intended for typesetting a root, while the latter is a function defined by pgfmath that actually calculates a square root. In addition, multiplication has to be explicit I think, so 4*\x, not 4\x.

As such, a working version of your snippet would be

\documentclass[border=2mm]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw [domain=0:4] plot ({\x},{2-sqrt{4*\x-\x*\x}});
\end{tikzpicture}
\end{document}

However, that is not a half circle of radius 2 centered on (2,2), which I guess is what you want.

The correct code for a full circle would be

\draw [domain=0:4,samples=200] plot ({\x},{2+sqrt(4-(\x-2)^2))})
                               plot ({\x},{2-sqrt(4-(\x-2)^2))});

Due to some roundoff problems, this does unfortunately not plot a full circle, I expect there is no point exactly at x=4. A way around that is to use the samples at key to ensure that the endpoints of the interval has a point, i.e.

\draw [samples at={0,0.01,...,3.99,4}] plot ({\x},{2+sqrt(4-(\x-2)^2))})
                                       plot ({\x},{2-sqrt(4-(\x-2)^2))});

A more powerful way of plotting such implicit functions is to use gnuplot as in How to plot smoothly an implicit function using gnuplot and tikz-pgf? The code for the equation in your question would be as below. gnuplot must be installed, and you have to compile with --shell-escape, e.g. pdflatex --shell-escape filename.tex.

\begin{tikzpicture}
    \draw plot[id=curve, raw gnuplot] function{
      f(x,y) = (y-2)**2 + (x-2)**2 - 4;
      set xrange [0:4];
      set yrange [0:4];
      set view 0,0;
      set isosample 1000,1000;
      set cont base;
      set cntrparam levels discrete 0;
      unset surface;
      splot f(x,y)
    };
\end{tikzpicture}

Of course, by far the simplest way of drawing a circle is \draw (2,2) circle[radius=2]; but that doesn't apply to more general functions.

Complete code and output:

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw [domain=0:4,samples=200] plot ({\x},{2+sqrt(4-(\x-2)^2))})
                               plot ({\x},{2-sqrt(4-(\x-2)^2))});

\node at (2,2) {1};
\end{tikzpicture}
\begin{tikzpicture}
\draw [samples at={0,0.01,...,3.99,4}] plot ({\x},{2+sqrt(4-(\x-2)^2))})
                                       plot ({\x},{2-sqrt(4-(\x-2)^2))});
\node at (2,2) {2};
\end{tikzpicture}

\begin{tikzpicture}
    \draw plot[id=curve, raw gnuplot] function{
      f(x,y) = (y-2)**2 + (x-2)**2 - 4;
      set xrange [0:4];
      set yrange [0:4];
      set view 0,0;
      set isosample 1000,1000;
      set cont base;
      set cntrparam levels discrete 0;
      unset surface;
      splot f(x,y)
    };
\node at (2,2) {3};
\end{tikzpicture}
\begin{tikzpicture}
\draw (2,2) circle[radius=2];
\node at (2,2) {4};
\end{tikzpicture}
\end{document}