\documentclass[border=2pt]{standalone}

% Drawing
\usepackage{tikz}

% Tikz Library
\usetikzlibrary{decorations.markings, calc}

% Notation
\usepackage{physics}

% Newcommand
%% Midline Label
\newcommand{\midlinelabel}[3]{
   \node[inner sep = 1.3pt] (midlabel) at ($ (#1)!.5!(#2) $) {#3};
   \draw[thick, line cap = round] (#1) --  (midlabel);
   \draw[-latex, thick, line cap = round] (midlabel) -- (#2);
}

% Styles
%% Arrows
\tikzset{arrow/.style = {postaction=decorate, decoration={markings,mark=between positions 0.1 and 0.9 step 3cm with \arrow{stealth}}}}

\begin{document}
	
	% Macros
	\def\a{5}
	\def\b{3}
	\def\Theta{atan(\b/\a)}
	\def\r{1}
	\def\sm{0.17}
	
	\begin{tikzpicture}
			%Grid
%			\draw[thin, dotted] (-1,-1) grid (10,10);
%			\foreach \i in {1,...,8}
%			{
%				\node at (\i,-2ex) {\i};	
%			}
%			\foreach \i in {1,...,8}
%			{
%				\node at (-2ex,\i) {\i};	
%			}
%			\node at (-2ex,-2ex) {0};
			
			% Rotate the Hyperbola
			\begin{scope}[rotate=-\Theta]
				% Dashed Axis
				\draw[domain=-2:8, dashed] plot (\x,{\b/\a*\x});
				\draw[domain=1.5:-4, dashed] plot (\x,{-\b/\a*\x});	
				% Plot
				\draw[domain=40:-22, samples=100, thick, blue, -stealth, arrow] plot ({\sm*\x},{\sm*\b*sqrt(1+(\x)^(2)/(\a)^2)});
				% r_o
				\midlinelabel{$(0,0)+(90:-1.17)$}{0,\sm*\b}{$r_o$}
			\end{scope}
			
			% Angles
			\draw[-latex, thick] (-\r,0) arc (180:(90+\Theta):\r) node[pos=0.6, left] {$\theta$};
			
			% Particle
			\draw[-latex, thick, red] (10,0) -- +(-1.2,0) node [above, shift={(0.1,0.1)}] {$\vb{v}$};
			\draw[fill=black] (10,0) circle [radius=2pt] node [above, shift={(0,0.2)}] {$m$};
			
			% Node
			\node[blue] at (-0.8,3) {Orbit};
			
			% Vectors
			\midlinelabel{-0.6,-1}{10,0}{$\vb{r}_\infty$}
			\midlinelabel{-0.6,-1}{-0.6,0}{$b$}
			
			% Point 
			\draw[fill=black] (-0.6,-1) circle [radius=1.5pt] node [below, shift={(0,-0.1)}] {$\mathrm{O}$};
	\end{tikzpicture}
	
\end{document}