added image of quadratic function and a point that has two points on the function with minimal distance

tikz/2d-x-square-with-circle/2d-x-square-with-circle.tex

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+\documentclass[varwidth=true, border=2pt]{standalone}
+
+\usepackage{pgfplots}
+\usepackage{tikz}
+
+\begin{document}
+\begin{tikzpicture}
+    \begin{axis}[
+        legend pos=south west,
+        axis x line=middle,
+        axis y line=middle,
+        grid = major,
+        %width=9cm,
+        %height=9cm,
+        grid style={dashed, gray!30},
+        xmin=-1.5,     % start the diagram at this x-coordinate
+        xmax= 1.5,    % end   the diagram at this x-coordinate
+        %ymin=-0.25,     % start the diagram at this y-coordinate
+        %ymax= 2.25,   % end   the diagram at this y-coordinate
+        axis background/.style={fill=white},
+        xlabel=$x$,
+        ylabel=$y$,
+        %xticklabels={-2,-1.6,...,7},
+        %yticklabels={-8,-7,...,8},
+        tick align=outside,
+        minor tick num=-3,
+        enlargelimits=true,
+        tension=0.08]
+      \addplot[domain=-1.5:1.5, red, thick,samples=50] {x*x}; 
+	\draw[blue, thick] \pgfextra{
+	  \pgfpathellipse{\pgfplotspointaxisxy{0}{1}}
+		{\pgfplotspointaxisdirectionxy{0.87}{0}}
+		{\pgfplotspointaxisdirectionxy{0}{0.87}}
+	  % see also the documentation of 
+	  % 'axis direction cs' which
+	  % allows a simpler way to draw this ellipse
+	};
+    \end{axis} 
+\end{tikzpicture}
+\end{document}

tikz/2d-x-square-with-circle/Makefile

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+SOURCE = 2d-x-square-with-circle
+DELAY = 80
+DENSITY = 300
+WIDTH = 512
+
+make:
+	pdflatex $(SOURCE).tex -output-format=pdf
+	make clean
+
+clean:
+	rm -rf  $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot
+
+gif:
+	pdfcrop $(SOURCE).pdf
+	convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif
+	make clean
+
+png:
+	make
+	make svg
+	inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png
+
+transparentGif:
+	convert $(SOURCE).pdf -transparent white result.gif
+	make clean
+
+svg:
+	#inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg
+	pdf2svg $(SOURCE).pdf $(SOURCE).svg
+	# Necessary, as pdf2svg does not always create valid svgs:
+	inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg

tikz/2d-x-square-with-circle/Readme.md

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+Compiled example
+----------------
+![Example](2d-x-square-with-circle.png)