codice prima figura
\begin{tikzpicture}
\begin{axis}[
width = 0.7\textwidth,
height = 0.7\textwidth,
xtick = \empty,
ytick = \empty,
axis on top,
axis equal image,
axis x line=center,
axis y line=center,
xmin = -3.5,
xmax = 3.5,
ymin = -3.5,
ymax = 3.5,
xlabel = {$x$},
ylabel = {$y$},
ylabel style={anchor=north east},
extra x ticks = {0},
extra x tick label = {$\hspace{0.4cm}O$},
disabledatascaling,
]
\draw[thick,red,fill=YellowOrange] (axis cs:0,0) ellipse [x radius=2, y radius=1,rotate=180];
\addplot[mark=*] coordinates {(2,0)} node[below right] {$(2,0)$};
\addplot[mark=*] coordinates {(-2,0)} node[below left] {$(-2,0)$};
\addplot[mark=*] coordinates {(0,1)} node[above right] {$(0,1)$};
\addplot[mark=*] coordinates {(0,-1)} node[below right] {$(-1,0)$};
\end{axis}
\end{tikzpicture}
seconda figura
codice seconda figura
\begin{tikzpicture}
\begin{axis}[
width = 0.7\textwidth,
height = 0.7\textwidth,
xtick = \empty,
ytick = \empty,
axis on top,
axis equal image,
axis x line=center,
axis y line=center,
xmin = -3.5,
xmax = 4.5,
ymin = -3.5,
ymax = 3.5,
xlabel = {$x$},
ylabel = {$y$},
ylabel style={anchor=north east},
extra x ticks = {0},
extra x tick label = {$\hspace{0.4cm}O$},
disabledatascaling,
]
\addplot[mark=*,red] coordinates {(0,0) (-1,{sqrt(3)/2})};
\addplot[mark=*,red] coordinates {(0,0) (-1,- {sqrt(3)/2})};
\addplot[mark=*,red] coordinates {(0,0) (-2,0)};
\addplot[mark=*,red] coordinates {(0,0) (2,0)};
\draw[thick,red] (axis cs:0,0) ellipse [x radius=2, y radius=1,rotate=180];
\draw (axis cs:-1,1.4) node[red] {$t=\frac{2}{3}\pi$};
\draw (axis cs:-1,-1.4) node[red] {$t=\frac{4}{3}\pi$};
\draw (axis cs:-2.6,0.4) node[red] {$t=\pi$};
\draw (axis cs:2.8,0.4) node[red] {$t=0,\,2\pi$};
\end{axis}
\end{tikzpicture}
terza figura
codice terza figura
\begin{tikzpicture}
\begin{axis}[
width = 0.7\textwidth,
height = 0.7\textwidth,
xtick = \empty,
ytick = \empty,
axis on top,
axis equal image,
axis x line=center,
axis y line=center,
xmin = -3.5,
xmax = 4.5,
ymin = -3.5,
ymax = 3.5,
xlabel = {$x$},
ylabel = {$y$},
ylabel style={anchor=north east},
extra x ticks = {0},
extra x tick label = {$\hspace{0.4cm}O$},
disabledatascaling,
]
\addplot[mark=*,red] coordinates {(0,0) (-1,{sqrt(3)/2})};
\addplot[mark=*,blue] coordinates {(0,0) (-0.25,0)};
\addplot[mark=*,red] coordinates {(0,0) (-1,- {sqrt(3)/2})};
\addplot[mark=*,red] coordinates {(0,0) (-2,0)};
\addplot[mark=*,red] coordinates {(0,0) (2,0)};
\draw[thick,red,fill=YellowOrange] (axis cs:0,0) ellipse [x radius=2, y radius=1,rotate=180];
\draw (axis cs:-0.25,-0.25) node[blue] {$P_1$};
\draw (axis cs:-1,1.4) node[red] {$P_4$};
\draw (axis cs:-1,-1.4) node[red] {$P_5$};
\draw (axis cs:-2.6,0.4) node[red] {$P_3$};
\draw (axis cs:2.8,0.4) node[red] {$P_2$};
\end{axis}
\end{tikzpicture}
quarta figura
codice quarta figura
\begin{tikzpicture}
\begin{axis}[
width = 0.7\textwidth,
height = 0.7\textwidth,
axis on top ,
xtick = \empty,
ytick = \empty,
axis equal image,
axis x line=center,
axis y line=center,
xmin = -6,
xmax = 6,
ymin = -4,
ymax = 7,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{0.4cm}0$},
y label style={anchor=north east}
]
\addplot[mark=*,very thick,red] coordinates { (-1,-1) (-1,4) (1.5,-1)(-1,-1)};
\addplot[mark=*] coordinates {(-1,-1)} node[below left] {$B=(-1,-1)$};
\addplot[mark=*] coordinates {(-1,4)} node[below left] {$A=(-1,4)$};
\addplot[mark=*] coordinates {(1.5,-1)} node[below right] {$\,\,C=\left(\dfrac{3}{2},-1\right)$};
\addplot[very thick,dashed,samples=100,domain=3:-3,red,,name path=retta 1] {-2*x+2};
\addplot[very thick,samples=100,domain=3:-3,red,dashed,,name path=retta 2] {-1};
\addplot[very thick,red,dashed] coordinates { (-1,4) (-1,6)};
\addplot[very thick,red,dashed] coordinates { (-1,-1) (-1,-5)};
\addplot[TealBlue!30] fill between[of=retta 1 and retta 2, soft clip={domain=-1:1.5}];
\draw (axis cs:-2,-2.5) node[red] {$x=-1$};
\draw (axis cs:1.5,-3.5) node[red] {$y=-2x+2$};
\draw (axis cs:2.4,-0.7) node[red] {$y=-1$};
\draw (axis cs:1.4,1.4) node[rotate=0] [red]{$\partial E$};
\draw (axis cs:-0.3,0.4) node[rotate=0] [BlueViolet]{$E^\circ$};
\end{axis}
\end{tikzpicture}
quinta figura
codice quinta figura
\begin{tikzpicture}
\begin{axis}[
width = 0.7\textwidth,
height = 0.7\textwidth,
xtick = \empty,
ytick = \empty,
axis on top,
axis equal image,
axis x line=center,
axis y line=center,
xmin = -4,
xmax = 4,
ymin = -4,
ymax = 4,
xlabel = {$x$},
ylabel = {$y$},
extra x tick label = {$\hspace{0.4cm}O$},
disabledatascaling,
]
\draw[thick,red,fill=Lavender] (axis cs:0,0) circle [radius=2];
\addplot[mark=*] coordinates {(2,0)} node[below right] {$(2,0)$};
\addplot[mark=*] coordinates {(-2,0)} node[below left] {$(-2,0)$};
\addplot[mark=*] coordinates {(0,2)} node[above right] {$(0,2)$};
\addplot[mark=*] coordinates {(0,-2)} node[below right] {$(0,-2)$};
\draw (axis cs:0.3,0.25) node[rotate=0] {$A^\circ$};
\draw (axis cs:2.3,1.4) node[rotate=0] [red]{$\partial A$};
\end{axis}
\end{tikzpicture}