如何画圆的切线和法线？

Question

我想画一条圆的切线和法线，如下图所示：

我写的编码如下：

\begin{figure}[h!]
    \centering
    \begin{tikzpicture}
    \node (c) at  (2,2) {$c$};
    \coordinate (O) at (0,0);
    \coordinate (A) at (2,2);
    \coordinate (P) at (3,3.2);
    \draw[->,thick] (-1,0)--(4,0) node[right]{$x$};
    \draw[->,thick] (0,-1)--(0,4) node[above]{$y$};
    \draw (O) node [below left]{$0$};
    \draw (2, 2) circle[radius = 1.5cm];
    \foreach \i in {45}{
        \draw (2, 2) --++ (\i:1.5cm);
    }

    \draw [fill=black] (A) circle (1pt);
    \end{tikzpicture}
\end{figure}

从而产生。

谁都行，请帮忙。

Answer 1

对于圆圈来说这非常容易。

\documentclass[tikz,border=3mm]{standalone}
\begin{document}
    \begin{tikzpicture}[>=stealth,font=\sffamily]
    \path (2,2) coordinate[label=below:$c$](c);
    \coordinate (O) at (0,0);
    \coordinate (P) at (3,3.2);
    \draw[->,thick] (-1,0)--(4,0) node[right]{$x$};
    \draw[->,thick] (0,-1)--(0,4) node[above]{$y$};
    \draw (O) node [below left]{$0$};
    \draw (c) circle[radius = 1.5cm];
    \foreach \i [count=\X] in {45}{
        \draw (c) --++ (\i:1.5cm) coordinate (x\X);
        \draw (x\X) -- ++ (\i:1) node[pos=0.8,below right]{normal}; % normal
        \draw (x\X) ++ (\i+90:1) -- ++ (\i-90:2)
        node[pos=0.9,above right]{tangent}; % tangent
    }

    \draw [fill=black] (c) circle (1pt);
    \end{tikzpicture}
\end{document}

注意 Ti钾Z 提供了更多选项，例如tangent cs:，请参阅部分13.2.4 切线坐标系pgfmanual v3.1.4。

Answer 2

(p1)--(p2)要在点处绘制线的法线(p1)，

\draw ($(p1)!1!-90:(p2)$) -- ($(p1)!1!90:(p2)$);

\documentclass[border=3mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
    \centering
    \begin{tikzpicture}
    \node (c) at  (2,2) {$c$};
    \coordinate (O) at (0,0);
    \coordinate (A) at (2,2);
    \coordinate (P) at (3,3.2);
    \draw[->,thick] (-1,0)--(4,0) node[right]{$x$};
    \draw[->,thick] (0,-1)--(0,4) node[above]{$y$};
    \draw (O) node [below left]{$0$};
    \draw (2, 2) circle[radius = 1.5cm];
    \foreach \i in {45}{
        \draw (2, 2) --++ (\i:1.5cm)coordinate(p\i){};
        \draw ($(p\i)!1!-90:(2,2)$) -- ($(p\i)!1!90:(2,2)$);
    }

    \draw [fill=black] (A) circle (1pt);

    \end{tikzpicture}
\end{document}