Grafici con Tikz numero 11 (grafici di geometria analitica)

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Prima di ogni figura ricordare di mettere

\documentclass[usenames,dvipsnames]{article}
\usepackage{pgfplots}

prima figura

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codice prima figura

\begin{tikzpicture}
\begin{axis}[
width = 0.8\textwidth,
height =0.8\textwidth,
xtick = \empty,
axis equal image,
ytick = \empty,
axis equal image,
axis x line=center,
axis y line=center,
xmin = -8,
xmax =12,
ymin = -6,
ymax = 6,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{0.6cm}0$},
y label style={anchor=north east}
]
\addplot[very thick,samples=100,domain=-8:9,
green] {-1/3*x^2+4/3*x+5/3};
\addplot[samples=100,domain=-6:40,very thick,red] {2*x+2};
\draw (axis cs:-4.5,-2.5) node {$t:y=2x+2$};
\addplot[mark=*] coordinates {(5,0)} node[above right] {$B$};
\addplot[mark=*] coordinates {(-1,0)} node[above right] {$A$};
\draw (axis cs:8.8,-1) node {$\gamma:y=-\frac{1}{3}x^2+\frac{4}{3} x+\frac{5}{3}$};
\end{axis}
\end{tikzpicture}

seconda figura

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codice seconda figura

\begin{tikzpicture}
\begin{axis}[
width = 0.8\textwidth,
height = 0.8\textwidth,
xtick = \empty,
axis equal image,
ytick = \empty,
axis equal image,
axis x line=center,
axis y line=center,
xmin = -10,
xmax =20,
ymin = -5,
ymax = 10,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.6cm}0$},
y label style={anchor=north east}
]
\addplot[red, very thick] (x*x-6*x,x);
\addplot[samples=100,domain=-6:50,very thick,red] {3+sqrt(x+9)};
\draw (axis cs:10,-4) node {$\gamma:\ x=y^2-6y$};
\addplot[mark=*] coordinates {(0,6)} node[above right] {$P$};
\addplot[mark=*] coordinates {(-9,3)} node[below left] {$V$};
\end{axis}
\end{tikzpicture}
terza figura

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codice terza figura

\begin{tikzpicture}
\begin{axis}[
set layers,
disabledatascaling,
axis equal image,
scale=0.75,
axis x line=center,
axis y line=center,
xmin = 0,
xmax = 6.9,
ymin = 0,
ymax = 6.9,
xlabel = {$x$},
ylabel = {$y$},
xtick={1,2,3,4,5,6,7},
ytick={1,2,3,4,5,6},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.45cm}O$},
extra y ticks = {0},
extra y tick label = {\ },
grid=major,
grid style={line width=1pt, draw=gray!30}
]

\addplot[mark=*,very thick] coordinates {(1,5) (3,4) (5,3) (4,6) (2,2) (5,3)};
\addplot[mark=*,very thick] coordinates {(2,2) (1,5) (4,6)};
\addplot[mark=*,blue] coordinates {(3,4)} node[above] {$C\ \phantom{\big|}$};
\addplot[no marks] coordinates {(1,5)} node[above] {$(1,5)\ $};
\addplot[mark=o,red,very thick, mark size=5pt] coordinates {(2,2)} node[below] {$(2,2)\rule{0pt}{10pt}$};

\addplot[mark=x,Gray,draw=none,mark size=2.5pt] coordinates {(1,3) (5,5) (4,2) (5,2)};
\end{axis}
\end{tikzpicture}

quarta figura

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codice quarta figura

\begin{tikzpicture}
\begin{axis}[
axis on top,
width=0.75\textwidth,
height=0.5\textwidth,
axis x line=center,
axis y line=center,
xmin = -2.9,
xmax = 2.9,
ymin = -0.9,
ymax = 6.9,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.45cm}\phantom{/}O\phantom{/}$},
]
\path[name path=axis] (axis cs:0,0) -- (axis cs:2,0);
\addplot[very thick,samples=100,BurntOrange,domain=0:4,name path=tangent] {4+4*(x-2)};
\addplot[very thick,samples=100,DarkOrchid,domain=0:4,name path=parabola] {x^2};
\addplot[very thick,samples=100,DarkOrchid,domain=-4:0,densely dashed] {x^2};
\addplot[TealBlue!50]fill between[of=axis and parabola, soft clip={domain=0:1}];
\addplot[TealBlue!50]fill between[of=tangent and parabola, soft clip={domain=1:2}];
\addplot[SkyBlue!20]fill between[of=axis and tangent, soft clip={domain=1:2}];
\addplot[no marks,very thick,dotted] coordinates {(-2,0) (-2,4) (2,4) (2,0)};
\addplot[mark=*,WildStrawberry,mark size=3pt] coordinates {(2,4)} node[right] {$\ (a,a^2)$};
\addplot[mark=*] coordinates {(1,0)} node[above right] {$\ \ a/2$};
\addplot[mark=*] coordinates {(2,0)};
\addplot[no marks] coordinates {(0.8,0.35)} node {$\mathcal{A}$};
% \addplot[no marks] coordinates {(-2.4,6.4)} node[right] {esempio: $a=2$};
\end{axis}
\end{tikzpicture}

quinta figura

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codice quinta figura

\begin{tikzpicture}
\begin{axis}[
width=0.7\textwidth,
height=0.4\textwidth,
axis x line=center,
axis y line=center,
xmin = 0,
xmax = 1.9,
ymin = 0,
ymax = 4.9,
xlabel = {$r$},
ylabel = {$\mathcal{A}$},
xtick = {1,sqrt(2)},
xticklabels = {$\phantom{\sqrt{2}}1\phantom{\sqrt{2}}$,$\sqrt{2}$},
ytick = {1,2,3,4},
extra x ticks = {0},
extra x tick label = {$O$},
]

\addplot[very thick,dotted,no marks] coordinates {(1,0) (1,10)};
\addplot[very thick,dotted,no marks] coordinates {(sqrt(2),0) (sqrt(2),10)};

\addplot[very thick,samples=100,blue,domain=0:1] {0};
\addplot[very thick,samples=50,blue,domain=1:1.414] {4*(x^2*acos(1/x)/180*pi - sqrt(x^2-1)};
\addplot[very thick,samples=100,blue,domain=1.414:5] {pi*x*x-4};

\addplot[very thick,samples=100,BurntOrange,domain=0:1] {4-pi*x*x};
\addplot[very thick,samples=50,BurntOrange,domain=1:1.414] {4*(-x^2*(pi/4-acos(1/x)/180*pi) + 1 - sqrt(x^2-1)};
\addplot[very thick,samples=100,BurntOrange,domain=1.414:5] {0};

\addplot[very thick,samples=100,ForestGreen,domain=0:1] {4-pi*x*x};
\addplot[very thick,samples=50,ForestGreen,domain=1:1.414] {4*(2*x^2*acos(1/x)/180*pi - 2*sqrt(x^2-1) + 1 - pi*x*x/4)};
\addplot[very thick,samples=100,ForestGreen,domain=1.414:5] {pi*x*x-4};

\addplot[no marks,blue] coordinates {(0.5,0.5)} node {$A(r)$};
\addplot[no marks,BurntOrange] coordinates {(1.6,0.5)} node {$B(r)$};
\addplot[no marks,ForestGreen] coordinates {(0.6,3.4)} node[rotate=-33] {$A(r)+B(r)$};
\end{axis}
\end{tikzpicture}