绘制椭圆交点

Question

我正在尝试绘制两个椭圆的交点，但它们似乎偏离了。

我的代码：

\documentclass [10pt] {article}
\usepackage{pgfplots}
\usepackage{tikz}
\usetikzlibrary{patterns}
\begin{document}
    \begin{tikzpicture}
        \begin{scope}
            \clip (0,0) ellipse (1cm and 3cm);
            \fill [blue,pattern=north east lines] (0,0) ellipse (3cm and 1cm);
        \end{scope}     
        \draw[red] (0,0) ellipse (3cm and 1cm);
        \draw[blue] (0,0) ellipse (1cm and 3cm);
        \draw[step=1cm,gray,very thin,dashed,] (-2.9,-2.9) grid (2.9,2.9);
        \draw[<->,thick] (-3.2,0) -- (3.2,0);
        \draw[<->,thick] (0,-3.2) -- (0,3.2);
        \draw (0.866,0.866) circle (0.5ex)[fill=black]node[anchor=south west, black]{$(\frac{\sqrt{3}}{2},\frac{\sqrt{3}}{2})$};
\end{tikzpicture}
\end{document}

以下是该问题的图片：

为了确保我没有发疯，我检查了WolframAlpha。

我怎样才能准确地绘制我需要的点？

Answer 1

你应该再检查一下你的数学。我不知道你真正想要什么，但这里有一个正确的解决方案，它与你在 WolframAlpha 上使用的公式相匹配。

\documentclass[10pt]{article}
\usepackage{pgfplots}
\usepackage{tikz}
\usetikzlibrary{patterns}
\begin{document}
    \begin{tikzpicture}
        \begin{scope}
            \clip (0,0) ellipse (1 and 1.732050808);
            \fill [blue,pattern=north east lines] (0,0) ellipse (1.732050808 and 1);
        \end{scope}     
        \draw[red] (0,0) ellipse (1.732050808 and 1);
        \draw[blue] (0,0) ellipse (1 and 1.732050808);
        \draw[step=1,gray,very thin,dashed,] (-2.9,-2.9) grid (2.9,2.9);
        \draw[<->,thick] (-3.2,0) -- (3.2,0);
        \draw[<->,thick] (0,-3.2) -- (0,3.2);
        \draw (0.866,0.866) circle (0.5ex)[fill=black]node[anchor=south west, black]{$\left(\frac{\sqrt{3}}{2},\frac{\sqrt{3}}{2}\right)$};
\end{tikzpicture}
\end{document}

输出：

Answer 2

您可以使用intersections库tikz来获取真实的交点。我建议您仔细检查数学运算以确保计算出的坐标准确无误。

\documentclass [10pt] {article}
\usepackage{tikz}
\usetikzlibrary{patterns,intersections}
\begin{document}
    \begin{tikzpicture}[x=1cm,y=1cm]
    \pgfmathsetmacro{\intp}{sqrt(3)/2.0};
        \begin{scope}
            \clip (0,0) ellipse (1cm and 3cm);
            \fill [blue,pattern=north east lines] (0,0) ellipse (3cm and 1cm);
        \end{scope}     
        \path[draw,red,name path=p1] (0,0) ellipse (3cm and 1cm);
        \path[draw,blue,name path=p2] (0,0) ellipse (1cm and 3cm);
        \draw[step=1cm,gray,very thin,dashed,] (-2.9,-2.9) grid (2.9,2.9);
        \draw[<->,thick] (-3.2,0) -- (3.2,0);
        \draw[<->,thick] (0,-3.2) -- (0,3.2);
        \path [name intersections={of=p1 and p2}];
        \draw (intersection-1) circle (0.5ex)[fill=black]node[anchor=south west, black]{$(\frac{\sqrt{3}}{2},\frac{\sqrt{3}}{2})$};
\end{tikzpicture}
\end{document}