how to shade an region bounded by curves

In luadraw (which produces TikZ) there is a dedicated method for this type of drawing: Ddomain2

\documentclass{standalone}%compile with lualatex only \usepackage[svgnames]{xcolor} \usepackage{luadraw}%https://github.com/pfradin/luadraw/ \usepackage{fouriernc} %https://tex.stackexchange.com/questions/755217/how-to-shade-an-region-bounded-by-curves \begin{document} \begin{luadraw}{name=shade_region} local g = graph:new{} local f = function(x) return 1/x end local h = function(x) return -1/x end g:Ddomain2(f,h,{x={-1,4},draw_options="fill=pink"}) g:Daxes({0,1,1}) g:Linewidth(8) g:Dcartesian(h,{draw_options="red",discont=true}) local a,b = 1.5*Z(1,1.5), Z(3,1) g:Beginclip({a,0,b,"l"}) g:Ddomain1(f,{x={0,4},draw_options="draw=none,fill=green,fill opacity=0.3"}) g:Endclip() g:Dcartesian(f,{draw_options="blue",discont=true}) g:Dpath({a,0,b,"l"}) g:Show() \end{luadraw} \end{document} 

Maybe not the easiest way, but you can make use of the fillbetween library provided by the pgfplots package:

\documentclass{amsart} \usepackage{pgfplots} % loads tikz \pgfplotsset{compat=1.18} \usetikzlibrary{fillbetween, backgrounds} \begin{document} \begin{tikzpicture} \draw [name path=a, thick, domain=0.5:3] plot (\x, { 1.2/\x)}); \draw [name path=b, thick, domain=-3:-0.5] plot (\x, { 1.2/\x)}); \draw [name path=c, thick, domain=0.5:3] plot (\x, {-1.2/\x)}); \draw [name path=d, thick, domain=-3:-0.5] plot (\x, {-1.2/\x)}); \draw (-3.4,0) -- (3.4,0); \draw (0,-2.6) -- (0,2.6); \draw [name path=e, thick] (0,0) -- (2.2,2.2); \draw [name path=f, thick] (0,0) -- (3.1,1.5); \path [name path=ac, intersection segments={ of=a and c, sequence={R* -- L*[reverse]} }]; \path [name path=bd, intersection segments={ of=b and d, sequence={R*[reverse] -- L*} }]; \path [name path=ef, intersection segments={ of=e and f, sequence={R*[reverse] -- L*} }]; \begin{scope}[on background layer] \fill [red!50, name path=acbd, intersection segments={ of=ac and bd, sequence={R* -- L*} }] -- cycle; \fill [green!50, intersection segments={ of=acbd and ef, sequence={R2 -- L2} }] -- cycle; \end{scope} \end{tikzpicture} \end{document} 

Here's another way to solve this problem.
No additional packages are required, and in my opinion, everything is as simple as possible.

\documentclass{amsart} \usepackage{tikz} \usetikzlibrary{patterns} \begin{document} \begin{center} \begin{tikzpicture} % Parameters \def\C{1.2} \def\xmax{3.4} \def\ymax{2.5} % Minimum |x| such that |C/x| = \ymax \pgfmathsetmacro{\xmin}{\C / \ymax} % ≈ 0.48 % Hatch the star-shaped region — only within the visible window \fill[pattern=north east lines, pattern color=gray!60] plot[domain=\xmin:\xmax, samples=200, smooth] (\x, {\C/\x}) -- plot[domain=\xmax:\xmin, samples=200, smooth] (\x, {-\C/\x}) -- cycle; \fill[pattern=north east lines, pattern color=gray!60] plot[domain=-\xmin:-\xmax, samples=200, smooth] (\x, {\C/\x}) -- plot[domain=-\xmax:-\xmin, samples=200, smooth] (\x, {-\C/\x}) -- cycle; % Fill the central vertical strip between the two branches to close the region near the y-axis \fill[pattern=north east lines, pattern color=gray!60] (\xmin,\ymax) -- (-\xmin,\ymax) -- (-\xmin,-\ymax) -- (\xmin,-\ymax) -- cycle; % Sector in the first quadrant \pgfmathsetmacro{\xA}{sqrt(\C)} % intersection of y = x and xy = C \pgfmathsetmacro{\k}{1.5/3.1} \pgfmathsetmacro{\xB}{sqrt(\C / \k)} \pgfmathsetmacro{\yA}{\xA} \pgfmathsetmacro{\yB}{\k * \xB} % Hatch the sector (only the part within the visible region) \fill[pattern=horizontal lines, pattern color=red!90!black] (0,0) -- (\xB, { \C / \xB}) -- plot[domain=\xB:\xA, samples=100, smooth] (\x, {\C/\x}) -- (\xA, { \C / \xA }) -- cycle; % Hyperbolas (visible portions only) \draw[thick, domain=\xmin:\xmax] plot (\x, {\C/\x}); \draw[thick, domain=\xmin:\xmax] plot (\x, {-\C/\x}); \draw[thick, domain=-\xmax:-\xmin] plot (\x, {\C/\x}); \draw[thick, domain=-\xmax:-\xmin] plot (\x, {-\C/\x}); % Axes \draw[->] (-3.7,0) -- (3.7,0) node[right] {$x$}; \draw[->] (0,-2.8) -- (0,2.8) node[above] {$y$}; % Rays \draw[thick] (0,0) -- (2.2,2.2); \draw[thick] (0,0) -- (3.1,1.5); \end{tikzpicture} \end{center} \end{document} 

Purely for comparison, here is a version in plain Metapost. (Follow the link for tutorials and reference).

You need to compile this with lualatex to get the luamplib support.

\documentclass[border=5mm]{standalone} \usepackage{luamplib} \begin{document} \mplibtextextlabel{enable} \begin{mplibcode} beginfig(1); % make the hyperbola paths, starting with a half-hyperbola path h[]; numeric s, t, maxx; s = 1/16; t = 1.2; maxx = 3; h0 = ((t,1) for x = t+s step s until maxx: .. (x,t/x) endfor) scaled 30; % and the others are made by reflecting and then rotating h1 = subpath (length h0, 0) of h0 .. h0 reflectedabout(origin, (1,1)); h2 = h1 rotated 90; h3 = h2 rotated 90; h4 = h3 rotated 90; % the axes trimmed to the size of the hyperbolas path xx, yy; xx = (xpart point 0 of h3, 0) -- (xpart point 0 of h1, 0); yy = xx rotated 90; % two random rays in first quadrant path ray[]; ray1 = origin -- 100 dir 30; ray2 = ray1 rotated 28; % the "star" is just made by joining the hyperbolas path star_shaped_region; star_shaped_region = h1 -- h2 -- h3 -- h4 -- cycle; % now shade the star by drawing and then clipping for i = -200 step 4 until 200: draw (left--right) scaled 600 rotated 42 shifted (i, 0) withpen pencircle scaled 1/4 withcolor 2/3 red; endfor clip currentpicture to star_shaped_region; % the "buildcycle" macro helps to make the curved wedge path curved_wedge; curved_wedge = buildcycle(ray1, h1, ray2); % you need to fill the wedge using the "image" macro, so that the clip % only applies to the drawing inside the image... picture filled_wedge; filled_wedge = image( unfill curved_wedge; % <- leave this out if you prefer cross-hatching for i = -10 step 3 until 200: % smaller step makes lines closer draw (left--right) scaled 600 rotated -32 shifted (i, 0) withpen pencircle scaled 1/4 withcolor 2/3 blue; endfor clip currentpicture to curved_wedge; ); draw filled_wedge; % add the image to the picture % finally draw all the lines... draw ray1; draw ray2; draw h1; draw h2; draw h3; draw h4; draw xx; draw yy; endfig; \end{mplibcode} \end{document}