也可以考虑使用luadraw,提供了g:Shift和g:Rotate等方便的方法:
\documentclass{standalone}
\usepackage{luadraw}
\usepackage[svgnames]{xcolor}
\usepackage{fourier-otf}
\begin{document}
\begin{luadraw}{name=tilted_hyperbola}
local ld = luadraw
local Z, i = ld.cpx.Z, ld.cpx.I
local sinh, cosh = math.sinh, math.cosh
local g = ld.graph:new{window = {-6, 6, -4, 7}}
local left_branch = function(t) return Z(-2 * cosh(t), sinh(t)) end
local right_branch = function(t) return Z(2 * cosh(t), sinh(t)) end
local plot_hyperbola = function(opt)
g:Dline({0, 1}, "-Latex,ultra thick")
g:Dline({0, i}, "-Latex,ultra thick")
g:Dparametric(right_branch, {t = {-2.5, 2.5}, nbdots = 100,draw_options = opt})
g:Dparametric(left_branch, {t = {-2.5, 2.5}, nbdots = 100,draw_options = opt})
g:Dline({0, Z(1, 1 / 2)}, "dashed,"..opt)
g:Dline({0, Z(1, -1 / 2)}, "dashed,"..opt)
end
plot_hyperbola("teal")
g:Savematrix()
g:Shift(Z(-2, 2))
g:Rotate(45)
plot_hyperbola("magenta")
g:Restorematrix()
g:Show()
\end{luadraw}
\end{document}



















问 如何绘制坐标轴中倾斜的双曲线及其渐近线?